Question

If alpha and beta are the zeroes of the quadratic polynomial x2-6a+alpha ,find the value of 'a' if 3alpha+2beta =0.

Answer 1

Dear Student,

$\Rightarrow$x² - 6a + alpha = 0
Comparing it with ax² + bx + c = 0
We get, a = 1 , b = 0 , c = -6a + alpha

Sum of roots = - $\frac{\mathrm{b}}{\mathrm{a}}$ = alpha + beta = 0 $\Rightarrow$alpha = - beta ................... (1)
Product of roots = $\frac{\mathrm{c}}{\mathrm{a}}$ = alpha beta = -6a + alpha .................... (2)
$\Rightarrow$3 alpha + 2 beta = 0
$\Rightarrow$3 alpha + 2 (- alpha) = 0 (from (1) )
$\Rightarrow$alpha = 0

From (2) $\Rightarrow$
$\Rightarrow$- 6a + alpha = 0
$\Rightarrow$- 6a + 0 = 0
$\Rightarrow$a = 0

Regards