Question

find the zeros of the quadratic polynomial 3 X ^ 2 - 17 X + 24 and verify the relationship between the zeros and its coefficient​

Answer 1

Answer:

$\large{\underline{\boxed{\sf 3 \: and \: \dfrac{8}{3}}}}$

Step-by-step explanation:

Given polynomial ;

P(x) = 3x² - 17x + 24

We can find the zeros of the polynomial by splitting the middle term.

⇒ 3x² - 17x + 24

⇒ 3x² - 9x - 8x + 24

⇒ 3x(x - 3) - 8(x - 3)

⇒ (x - 3)(3x - 8)

By zero product rule ;

⇒ x = 3 or x = $\sf \dfrac{8}{3}$

Hence, the zeros of the quadratic polynomial is 3 and 8/3.

_______________________.

Verification;

$\bf Sum \: of \: zeroes = \frac{ - (coefficient \: of \: x)}{coefficient \: of \: {x}^{2} }$

$\implies \sf 3 + \frac{8}{3} = \frac{ - ( - 17)}{3} \\ \\ \implies \sf \frac{9 + 8}{3} = \frac{17}{3} \\ \\ \implies \sf \frac{17}{3} = \frac{17}{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \tt verified.}$

$\bf Product \: of \: zeros = \frac{constant \: term}{coefficient \: of \: x {}^{2} }$

$\implies \sf 3 \times \frac{8}{3} = \frac{24}{3} \\ \\ \implies \sf 8 = 8 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \tt verified.}$