Question

If the product of the zeroes of quadratic polynomial 3x² + 5x – K² is -9 then the value of the K is ?​

Answer 1

Answer:   3*sqrt(3)

This is the same as sqrt(27)

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Explanation:

We use one of Vieta's formulas. Specifically, we'll focus on the quadratic case and we're multiplying the roots.

Consider the roots r1 and r2 for the general quadratic ax^2+bx+c = 0

According to one of Vieta's formulas, we would say that

r1*r2 = c/a

In this case,

• a = 3
• c = -k^2

So we know that

r1*r2 = c/a

r1*r2 = (-k^2)/3

Set this equal to the desired product of -9 and solve for k

r1*r2 = -9

(-k^2)/3 = -9

-k^2 = 3(-9)

-k^2 = -27

k^2 = 27

k = sqrt(27)

k = sqrt(9*3)

k = sqrt(9)*sqrt(3)

k = 3*sqrt(3)