Question

If a and b are the zeroes of the quadratic polynomial x² - 6x + a, find the value of 'a'. If 3a + 2b = 20

Answer 1

x2 - 6x + a = 0 ----> Given Equation
A and B are the roots of the polynomial
Given = 3A + 2B = 20
B = A +B - A
Let co-efficient of - x2 = K = 1 , -6x = b = -6
We know that A + B = -b/K = - ( -6 / 1 ) = 6
=> 3A + 2( A + B - A) = 20
=> 3A + 2( 6 - A) = 20
=> 3A + 12 - 2A = 20
=> A = 20 - 12
=> A = 8

3A + 2B = 20
=> 3 * 8 + 2B = 20
=> 2B = 20 - 24
=> 2B = -4
=>B = -2

We know that A*B = c/a => -2 * 8 = 16 = a/K = a/1 = 16
=> a = 16