Question

if x= -2 is a root of the polynomial p(x)= -2x^4 -7x^3-3x^2-tx-10 then find the value of t

Answer 1

Answer: The value of 't' is -1

p(x) = -2x^4 - 7x³ -3x² - tx - 10 , x = -2

Now , consider the value of x as -2 as given in the question

p(-2) = -2(-2)^4 - 7(-2)³ - 3(-2)² - t(-2) - 10 = 0

To find the value of 't' we need consider p(x) = 0

P(-2) = -2(16) - 7(-8) - 12 + 2t - 10 = 0

p(-2) = -32 + 56 + 2t - 22 = 0

p(-2) = 24 + 2t - 22 = 0

p(-2) = 2 + 2t = 0

p(-2) = 2t = -2

p(-2) = t = -2÷2

p(-2) = t = -1

Thank you