Question

show that X=2 is a root of 2x3+x2_7x_6​

Answer 1

Step-by-step explanation:

if x= 2 is a root ( zeroes) of given polynomial

=> x-2=0 => x-2 divides this polynomial.

so substituting x= 2

2×2³+2²-7×2-6

= 16+4-14-6

= 20-20

= 0

hence remainder =0=> x-2 divides

=> x=2 is a root of the polynomial.

proved

Answer 2

$\bold\pink{2 {x}^{3} + {x}^{2} - 7x - 6 = 0}$

$\bold\red{= \frac{ - (constant \: term)}{coefficient \: of \: x^{3} }}$

$\bold\green{( - 1) \times (2) \times (a) = \frac{( - 6)}{2}}$

$\bold\purple{⇒ - 2a = 3}$

$\bold\orange{⇒a = \frac{ - 3}{2}}$