Question

If alpha and beta are the zeroes of the quadratic polynomial 2x^2 - 5x + 3, then find the value of 1/2 alpha + 1/2 beta


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Answer 1

Question

If 1/alpha and 1/beta are the zeroes of the quadratic polynomial 2x^2 - 5x + 3, then find the value of 1/2 alpha + 1/2 beta

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

A polynomial

X²+3√3+6

${\sf{\green{\underline{\large{To\:Find}}}}}$

• $\tt\dfrac{1}{\alpha}{+}\dfrac{1}{\beta}$

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Let the zeroes of the polynomial be$\tt\dfrac{1}{\alpha}{and}\dfrac{1}{\beta}$

Then,

$\tt\dfrac{1}{\alpha}{+}\dfrac{1}{\beta}\dfrac{-b}{a}$

&

$\tt\dfrac{1}{2\alpha}{\times}\dfrac{1}{2\beta}\dfrac{c}{a}$

Here,

• P(x)=2x²-5x+3

a=2

b=-5

C=3

☞

$\tt\dfrac{1}{\alpha}{+}\dfrac{1}{\beta}\dfrac{5}{2}$

&

$\tt\dfrac{1}{2\alpha}{\times}\dfrac{1}{2\beta}\dfrac{3}{2}$

Solving

$\tt\dfrac{1}{\alpha}{+}\dfrac{1}{\beta}=\dfrac{-b}{a}$

$\tt\implies\dfrac{{\alpha}{+}{\beta}}{2\alpha\beta}$

¶utting values

$\tt\implies\dfrac{{\alpha+\beta}}{2\alpha\beta}$

$\rightarrow\tt\dfrac{\frac{5}{2}}{2\times{\frac{3}{2}}}$

$\rightarrow\tt\dfrac{\frac{5}{2}}{2\times{\frac{3}{2}}}$

=>5/6