Question

Given that 3x²+x-6)(x+1) and 3x³+Kx+hx-6 are identical, find the values of k and h.

Answer 1

Correct Question :

Given that (3x²+x-6)(x+1) and 3x³+kx²+hx-6 are identical, find the values of k and h.

Answer :

k = 4, h = - 5

Step-by-step explanation :

Quadratic polynomial :-

• It is a polynomial of degree 2
• General form, ax² + bx + c
• Relationship between zeroes and coefficients :

Sum of zeroes = -b/a

Product of zeroes = c/a

Cubic polynomial :-

• It is a polynomial of degree 3
• General form, ax³ + bx² + cx + d
• Relationship between zeroes and coefficients :

Sum of zeroes = -b/a

Sum of the product of zeroes taken two at a time = c/a

Product of zeroes = -d/a

Given,

(3x² + x - 6)(x + 1) and 3x³+kx²+hx-6 are identical.

= (3x²+x-6)(x+1)

= 3x² (x+1) + x(x+1) - 6(x+1)

= 3x³ + 3x² + x² + x - 6x - 6

= 3x³ + 4x² - 5x - 6

= 3x³ + kx² + hx - 6

Compare both the equations,

k = 4, h = - 5