Question

If the zeroes of the quadratic polynomial x^2+(a+1)x+b are 2 and -3. Find the value of a and b​

Answer 1

Given, quadratic polynomial is f() = 2 − 8 +

Let a and b are the zeroes of the polynomial

Again given, the sum of the squares of zeroes of the quadratic polynomial = 40

=> a2 + b2 = 40

=> (a + b)2 - 2ab = 40

=> 82 - 2ab = 40 {from the polynomial}

=> 64 - 2ab = 40

=> 2ab = 64 - 40

=> 2ab = 24

=> ab = 24/2

=> ab = 12

Now, product of the roots = k/1

=> 12 = k/1

=> k = 12

So, the value of k is 12

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