Question

If alpha and beta are zeroes of x2-3x+q. What is the value of q, if 2 alpha+3 beta=15

Answer 1

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Answer 2

Answer:

The value of q is -54.

Step-by-step explanation:

Since, if a and b are the zeroes of a quadratic equation,

Then,

$a+b=-\frac{\text{Coefficient of }x}{\text{Coefficient of }x^2}$

$a.b=\frac{\text{Constant term}}{\text{Coefficient of }x^2}$

Given,

$\alpha$ and $\beta$ are zeroes of a quadratic equation $x^2-3x+q$

By the above property,

$\alpha+\beta=-\frac{-3}{1}\implies \alpha+\beta=3$ ------(1)

Also, given,

$2\alpha+3\beta=15$ --------(2),

Equation (2) - 2 × equation (1),

We get,

$\beta=9$

From equation (1),

$\alpha=-6$

Thus, -6 × 9 = q/1

⇒ q = -54