Question

Find the zeroes of the quadratic polynomial p(x) = ax2 - (a2 + 1)x + a and verify the
relationship between the zeroes and the coefficients.​

Answer 1

Answer:

g(x) = a(x2+1) – x(a2+1) We put g(x) = 0 ⇒ a(x2+1)–x(a2+1) = 0 ⇒ ax2 + a − a2x – x = 0 ⇒ ax2 − a2x – x + a = 0 ⇒ ax(x − a) − 1(x – a) = 0 ⇒ (x – a)(ax – 1) = 0 This gives us 2 zeros, for x = a and x = 1/a Hence, the zeros of the quadratic equation are a and 1/a. Now, for verification Sum of zeros = – coefficient of x / coefficient of x2 a + 1/a = – (-(a2 + 1)) / a (a2 + 1)/a = (a2 + 1)/a Product of roots = constant / coefficient of x2 a x 1/a = a / a 1 = 1 Therefore, the relationship between zeros and their coefficients is verified.Read more on Sarthaks.com - https://www.sarthaks.com/623563/g-x-a-x-2-1-x-a-2-1