If the polynomial 6x4 + 8x3- 5x2 + ax + +b is exactly divisible by the polynomial 2x2 - 5 - Maths - Polynomials

Question

If the polynomial 6x4 + 8x3-
5x2 + ax + +b is exactly divisible by the polynomial
2x2 - 5 , then find the value of a & b
pls do it urgently

Ajanta Trivedi · Accepted Answer

the given polynomial $6 x^{4} + 8 x^{3} - 5 x^{2} + a x + b$ is divisible by $2 x^{2} - 5$ .

let us write the division.

$2 x^{2} - 5 \begin{matrix} 3 x^{2} + 4 x + 5 \\ 6 x^{4} + 8 x^{3} - 5 x^{2} + a x + b \end{matrix}$

$\underset{̲}{6 x^{4} - 15 x^{2}} \times 8 x^{3} + 10 x^{2} \underset{̲}{8 x^{3} - 20 x} \times 10 x^{2} + 20 x + a x \underset{̲}{10 x^{2} - 25} \times (20 + a) x + 25 + b$

since $6 x^{4} + 8 x^{3} - 5 x^{2} + a x + b$ is divisible by $2 x^{2} - 5$ therefore remainder = 0.

thus $(20 + a) x + (25 + b) = 0$

therefore coefficient of x and constant term both must be zero.

$20 + a = 0 \Rightarrow a = - 20 25 + b = 0 \Rightarrow b = - 25$

hope this helps you.

cheers!!

If the polynomial 6x4 + 8x3- 5x2 + ax + +b is exactly divisible by the polynomial 2x2 - 5 , then find the value of a & b pls do it urgently

If the polynomial 6x⁴ + 8x³- 5x² + ax + +b is exactly divisible by the polynomial 2x² - 5 , then find the value of a & b

pls do it urgently