Question

if alpha and beta are the zeroes of quadratic polynomial x^2-6x+a.find a,if 3alpha+2beta=20​

Answer 1

x^2-6x+a

alpha and beta are the zeroes so

$\alpha + \beta = - \frac{b}{a }$

$\alpha + \beta = 6$

$\alpha = 6 - \beta$

$3 \alpha + 2 \beta = 20$

$3(6 - \beta ) + 2 \beta = 20$

$18 - 3 \beta + 2 \beta = 20$

$18 - \beta = 20$

$- \beta = 2$

$\beta = - 2$

$\alpha + \beta = 6$

$\alpha - 2 = 6$

$\alpha = 8$

$\alpha \beta = \frac{c}{a}$

-16=a

hope this will help u

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