Question

Show that -⅔and ⅗are the zeroes of the polynomial 15x²+x-6

Answer 1

Question:

Show that ⅔ and -⅗ are the zeroes of the polynomial 15x²+x-6

To prove:

To prove that ⅔ and -⅗ are the zeroes of the polynomial 15x²+x-6.

Step-by-step explanation:

$15 {x}^{2} + x - 6 = 0$

Product :- -90 = -10 × 9

Sum :- 1 = -10+9

$15 {x}^{2} - 10x + 9x - 6 = 0$

$5x(3x - 2) + 3(3x - 2) = 0$

$(3x - 2)(5x + 3) = 0$

$3x - 2 = 0 \: & \: 5x + 3 = 0$

$\boxed{x = \frac{2}{3} \: & \: \frac{ - 3}{5}}$

$Therefore \: the \: zeroes \: of \: the \: polynomial \: are \: \boxed{ \frac{2}{3} \: & \: \frac{ - 3}{5}}$

Hence proved.