Question

The product of the roots of a quadratic equation is 12 and the sum of the roots is -6. We are given that the equation is ax^2 +18x + c = 0. Find the values of the coefficients a and c.

Answer 1

Given :

We are given an equation ax² + 18x + c = 0 whose product and sum of the zeroes is 12 and -6.

To find :

We have to find the values of a and c.

Solution :

When we compare the equation ax² + 18x + c = 0 to ax² + bx + c = 0, we get :

• a = a
• b = 18
• c = c

We know that :

• Sum of zeroes (α + β) = -b/a = -6
• -(18)/a = -6
• -18 = -6a
• a = -18/-6
• a = 3

Also,

• Product of zeroes = c/a = 12
• c/3 = 12
• c = 12 × 3
• c = 36

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Therefore, the values of a and c in the equation ax² + 18x + c = 0 whose product and sum of the zeroes is 12 and -6 is 3 and 36 respectively.