Question

If alpha and beta are zeroes of x^2-3x+p what is the value of p if 2alpha +3beta=15

Answer 1

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Answer 2

Answer:

-54 is the required value of P.

Step-by-step explanation:

Explanation:

Given in the question, alpha and beta are the zeroes of $x^2 - 3x + p$.

And $2\alpha + 3\beta = 15$

So, from the question, $\alpha\ and\ \beta$ are the zeroes of the given  polynomial.

Step 1:

As we know,

sum of zeroes ($\alpha + \beta$) = $\frac{-coefficient\ of \ x}{coefficient of \ x^2}$ = $\frac{-b}{a}$ = $\frac{-(-3)}{1}$ = 3

Product of zeroes $\alpha \beta$ = $\frac{constant}{ coefficient \ of \ x^2}$ = $\frac{c}{a}$ = p

$(\alpha + \beta )$ = 3 ........(i) and

$2 \alpha + 3\beta$ = 15  .........(ii)

On solving (i) and (ii) we get,

2 (α + β) = 3

2α + 3β = 15    

-     -          -    

-β = - 9

⇒ β = 9

Now, on putting the value of $\beta$ = 9 in (i) we get,

$\alpha$ + 9 = 3

⇒$\alpha$ = 3 - 9 = -6

Step 2:

Now, from step 1 we have, $\alpha = -6 and\ \beta \ = 9$

Product of zeroes($\alpha \beta$) =  p

⇒ -6 × 9 = p

⇒ p = -54

Final answer:

Hence, -54 is the required value of P.

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