Question

Alpha + beta are the zeros of polynomial then p of x is equals to x square - 5 x + 6 find the value of alpha + beta minus 3 alpha beta

Answer 1

☆GIVEN:

¤ A quadratic polynomial

${x}^{2} - 5x + 6$

¤ alpha and beta as the zeroes of the polynomial.

☆TO FIND :

$\alpha + \beta - 3 \alpha \times \beta$

☆SOLUTION:

We know that ;

$\blue {sum \: of \: zeroes = \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} } = \frac{ - b}{a}}$

or

$\pink {product \: of \: zeroes = \frac{constant \: term}{coefficient \: of \: {x}^{2} } = \frac{c}{a}}$

now,

In the given quadratic equation;

a = 1

b = -5

c = 6

so,

☆$\red {\alpha + \beta = \frac{ - ( - 5)}{1} }$

$\huge\orange {\alpha + \beta = 5}$

☆$\pink { \alpha \times \beta = \frac{6}{1} }$

$\huge\purple {\alpha \times \beta = 6}$

putting the value ;

$\red {\alpha + \beta - 3 \times \alpha \times \beta}$

$5 - 3 \times 6 \\ 5 - 18 \\ \\ - 13$

FINAL ANSWER;

$- 13$