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QUESTION 16Compute the Discriminant_x2_ 3x-3=0 21-3~21...

Question

QUESTION 16Compute the Discriminant_x2_ 3x-3=0 21-3~21

QUESTION 16 Compute the Discriminant_ x2_ 3x-3=0 21 -3 ~21



Answers

Use the discriminant to determine the number and type of roots. Do not solve the equation. $$-3 x^{2}+2 x=21$$

All right, given the function on the white bottom, we want to evaluate the discriminate. So the discriminate. This delta, which is B squared minus four a, C and B squared or B, is to over three squared minus for a, which is 1/2, and then see which is negative. Three. This would be equal to 4/9 buying us. So times three, which is plus 12 over to, and we can try and add these two fractions. Um, we can simplify the fractions by finding the denominator, which is 18 buying into 18. That's too times four eight plus two in 89 nine tens 12. It's one more. Eight beach is 108 plus eight, which is 16 1 16 over eight, which gives us 14.5. So the discriminate is 14.5. So they just wanted us to do that. Andi, if you want to interpret, it, feels that we can say so. It means that that quadratic equation have got two distinct riel solutions

If we have the quadratic two X squared minus 11 X plus three equals zero, and we want to compute the discriminate. Think about the quadratic formula and what's under to the square root B squared minus for a C that is your discriminate. So if a is to B is negative 11 and C is three in this case, thin. The discriminative is B squared minus four times a times C, which is 97. So 97 is the discriminate, which means there are going to be to really solutions, and they're going to be irrational because the square root of 97 is irrational.

To consider the quadratic equation. WHYY goes to X squared plus six X minus three. It wants me to find the discriminative. So the discriminate is B squared minus for a C this'll quadratic equations already in standard form. So it seemed a plug in our value. So be a six. We have six square minus forward times to start a value. Times negative three I guess our discriminates gonna be equal. Thio, just simplify this further. 36 uh, plus four times two times three is 24 start discriminate is equal to 60.

So on this problem, we're gonna use discriminative first to you find out more information about this quadratic equation. So the discriminative going to B B squared minus four e c. Which is like the middle off, the scary in the quadratic equation. Our car drug formula. Ah, solution. So if the experiments created and zero, we know that there's two real roots. Um, so let's just let's just all for it right now. And if we know that is equal to zero, we know there's a repeated route. We know that it's less than zero. There's gonna be imaginary bits. So, uh, b squared here is 49 minus ah four times a, which is two times C, which is zero. And that's equal to 49 because 49 is, ah, greater than zero. We know that there's two real roots. We also know that the square root of 49 is equal to seven. So on top of nine of those two routes, there are two riel rational and unequal roots. Probably the best way to solve this would be factory. So if I factor on X term from this equation, I'll get two x plus seven and solving this quarter equation. I get that X can be zero and it can be minus seven over too. And those are my two solutions.


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