Question

10. A quadratic equation 12-67-16 = 0 has sum of roots equal to 6, then find product of roots
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Answer 1

Answer:

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Answer 2

The product of roots of the given equation is -4/3.

A quadratic equation is of the form ax^2 + bx + c = 0, where a, b and c are constants. The roots of the quadratic equation can be found using the quadratic formula which states that the roots of the equation are given by:

x = [-b ± √(b^2 - 4ac)]/2a

Given the quadratic equation 12x^2 - 67x - 16 = 0, we can use the quadratic formula to find the roots of the equation.

x = [-(-67) ± √((-67)^2 - 4(12)(-16))]/2(12)

x = [67 ± √(67^2 + 256)]/24

x = [67 ± √(4489 + 256)]/24

x = [67 ± √(4745)]/24

the sum of roots is given as 6, which means that x1+x2 = 6

We can use that sum of roots formula which is x1+x2 = -b/a = -(-67)/12 = 67/12 = 6

Product of roots is given as c/a = -16/12 = -4/3

So the product of roots of the given equation is -4/3.

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