Question

If alpha and beta are the zeroes of quadratic polynomial 2x^2+3x-6 , then find the value of alpha^2 and beta^2

Answer 1

2x²+x-6⇒2x²+4x-3x-6⇒2x(x+2)-3(x+2)⇒(2x-3)(x+2)⇒x=3/2 and x=-2let alpha = 3/2 and beta = -2so 2 alpha and 2 beta is ⇒ 2×3/2=3= 2 alpha and 2 beta = -4so now 2 alpha+ 2 beta = 3+(-4)=-1and 2 alpha × 2 beta = 3×(-4)= -12so are quadratic equation will be x² -( sum of zeroes)x + (product of zeroes)⇒x²-(-1)x+(-12)⇒x²+x-12