Question

If the zeros of the polynomial x³-15x²+kx-k-14 are in AP then find K ?​

Answer 1

Here is the shortest and easiest way to solve this question, Hope you will read carefully with explanation.

• Its zeroes are in A.P=} a-d,a,a+d (Let these be different zeroes of this polynomial as A.P)

• Alpha+beeta+gamma=-b/a [[-b=-(-15)=15 and a=1]]

• (a+d)+a+(a+d)=-b/a

a+a+a=15 (as -d and +d got cancelled)

3a=15

[a=5]

• Lets put the value of 'a' or we can say 'x' in the polynomial.

p(x)=x³-15x²+Kx-K-14

p(5)=(5)³-15(5)²+5K-K-14

p(5)=125-375+5K-K-14

p(5)=-250-14+5K-K

p(5)=-264+4K=0

-264=-4K

-264/-4=K

So, [K=66]

.Hope it will help you.