Question

if the zero of polynomial 3x²-px+2&4x²-qx-10 is 2,find the value 2p-3q

Answer 1

Given polynomials,
3x²-px+2
4x²-qx-10

(1) 3x²-px+2
Zero of the polynomial is 2.
x = 2

3x²-px+2 = 0
3(2)² - p(2) + 2 = 0
3(4)-2p+2 = 0
12-2p+2 = 0
2p = 14
p = 7

(2) 4x²-qx-10
Zero of the polynomial is 2.
x = 2
4x²-qx-10 = 0
4(2)² - q(2) - 10 = 0
4(4) - 2q - 10 = 0
16 - 2q - 10 = 0
2q = 6
q = 3

Therefore, p = 7,q = 3

2p-3q = 2(7) - 3(3)
= 14 - 9
= 5