Question

If a, B.y are zeroes of a polynomial f(x)=x²-3px² +qx-r such that 2ß = a +y then:​

Answer 1

qp - r = 2p

Step-by-step explanation:

Let α,β,γ are the three Zeroes of the polynomial.

Given : f(x) = x - 3px + qx - r

On comparing with ax + bx + cx + d ,

a = 1 , b = -3p , c = q , d = -r

α = a - d

β = a

γ = a+d

Sum of zeroes of cubic POLYNOMIAL = −b/a

α + β + γ = −b/a

(a - d) + a + (a + d) = -(-3p)/1

a + a + a = 3p

3a = 3p

a = p

Since, a is a zero of the polynomial f(x) , Therefore, f(a) = 0

a- 3pa+ qa - r = 0

On substituting a = p ,

p - 3p(p) + qp - r = 0

p - 3p + qp - r = 0

-2p+ qp - r = 0

qp - r = 2p