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Given that &, B and rare the roots of the equation 2x' _x? + [ = 0. determine the equationwhose roots areandNote: (aB) + (ay)' + (Bw)' (ay Ba y...

Question

Given that &, B and rare the roots of the equation 2x' _x? + [ = 0. determine the equationwhose roots areandNote: (aB) + (ay)' + (Bw)' (ay Ba ya)' _ 2 afxa + B+Y) (u + B+y) _ Z(a8 + ay + By)

Given that &, B and rare the roots of the equation 2x' _x? + [ = 0. determine the equation whose roots are and Note: (aB) + (ay)' + (Bw)' (ay Ba ya)' _ 2 afxa + B+Y) (u + B+y) _ Z(a8 + ay + By)



Answers

If both the roots of $a x^{2}+b x+c$ are zero, then find the value of $a, b, c$.

In this problem we have to find out the video of uh scared place. Be scared. And if A. And B. The F. And be rules of the equation which is given S. X. Care plus eggs Plus one equal to zero. So we know that the some of the root is A. Plus Be equal to -7. Out of a. So this is one and product of the route which is even to A. Into B. It went to one. No we know that A. Plus B. Hold scare equal to a scare. Plus be scared plus to a B. And a scary place. Be scared equal to a plus Be whole scale -2. A. B. I said no the available a scare plus be scared equal to A. Plus B. Is one and A. into b. s. one. So therefore a squared plus Be scared equal to 1 -2 and a scare. Bliss be scary. Will do minus but

We have given given to the equation and we have to find the value of B. And the rules of this equation on A. And this is the question that NPR thanks of the Great It's the. Okay now I have to be right. Disciplinarians so that I have a connecting with. Do you know after technology I will shift this X Radio on the other side of the equation. We will get extra minus A Plus one. Old X. Yes. A. B. And you've lost 20. All right. We can. No. He settled here now there's some of the routes. The some of the rules. It's a frisbee. Well he comes to minus the coefficient of X. Which is just dividing the coefficient of explorer. Just one here. So I can write it as a plus one Over one. So it can simply write it as a plus one. The negative has signed is here. And negative object that we cancel out each other. Since you have a question. No. The even being close to the present one minus A. In this age of trivia. This will cancel out each other. And we will have review. He was the one. Very pretty simple possession and pretty easy solution. Thank you

Okay, so in this question we are given to quadratic situation which is the first one is X square plus bx Plus C equals to zero. And the other one, the other one is X squared plus C, X plus A B equals two zero. It is given that both of these equations have a common route. These questions have a common route. Ok, so let's say the root of the roots of the first equation are alpha and beta. Okay. And Let's say the roots of the 2nd equation, Alberta and drama. Okay, now, yeah, we know that alpha blockers, Beta equals two minus B by A. And here is one. So it becomes my LSD. This is a question first and alpha beta equals to see A. Okay, this is another, this is capital. Mhm. Now this is second equation. Okay, similarly Alpha plus gamma equals minus C. This is a question of my heart And alpha and gamma equals two baby. Now we need to find an equation or let's say we need to prove that uh the other routes, the other routes of these equations former form a different quadratic equation. And the quadratic question is given that we have to prove, Okay, it's alpha. It's also Okay, now we need to prove that quality question. Okay, so what we have to do, our approach will be that we have to find a better place, Gamma. Okay. And we have to find beta and gamma because these two things will from the quadratic equation whose roots are beta and gamma. Okay, so now for finding beatable Osama, what we'll do first will put alpha in both of the equations. Okay, Alphaville satisfied about the equations. So let's see alpha squared plus beta, Alpha plus C equals to zero. And similarly alfa square plus alpha plus A B equals to zero. Now subtracting these two equations, what we get is B minus C into alpha plus A into c minus B Is equal to zero. From here, the value of alpha comes out to be okay? No, we know that alphabet to equals to see A. Okay, so from here we can say that bitter equals to see and alpha gamma equals to a B. So we can see that gamma equals to be Okay? So now we have the values of alpha, Beta and gamma. Okay, now we can clearly see that beta plus Gamma comes out to be be classy. Okay? And uh beta and gamma comes out to be busy. Okay? Now if we see in the equation, the uh the middle term, okay, the B plus C town is not in the form of B policy. Okay? It's in the form of A. Okay, so we have to bring B plus in the form of A. So what we'll do is we'll just uh put the value of alpha and the equation. Okay just put the value of alpha in this situation, putting the value of alpha, and the situation what we get is alpha, A squared plus B. A. The C equals to zero, which implies that A plus B plus C equals to zero. So from here, what we get is B plus equals two minus The value of people. S he comes out to be -8. So this will be close to minus. Okay now we have better plus gamma and we have better plus beta into gamma which was required. Okay now we can see that the quadratic question whose roots are beta and gamma is x squared minus X. Plus 20 plus X. Plus B C equals to zero. So this is the required equation. Thank you.

So here we are given a quarter education that is he X squared plus Be explicit is equal to zero. And it has given that the root of the roots of this quarter equation Yeah minus me and B minus C. Okay, so we asked to find out what is yeah minus being Do B minus C divided by c minus eight. We need to find out what is this. So here we can say that this alpha and this is better. Okay then some of the products, some of the routes will be equal to alpha plus beta. That is yeah minus B Plus B -C will be equal to -7 by it. That is B and B will get cancer. Maybe we will cancel that is C minus, they will be called to be by and similarly product of the roads will be equal to Yeah man has been do B minus C which is equal to see by. So yeah, mine has been to b minus c. Bye C minus A is equal to see by a divided by be by it. Which is equal to see baby


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