Question

If alpha and beta are zeros of a quadratic polynomial X square + bx + c then find a quadratic polynomial whose zeros are one by Alpha and one by beta

Answer 1

Answer: $cx^{2} +bx+1=0$

Step-by-step explanation:

GIVEN:-

$\alpha$ and $\beta$ are zeroes of the polynomial

$f(x)= x^{2} + bx + c$

we know that,

$\alpha$ + $\beta$ = -b, $\alpha$ × $\beta$ = c

$(\frac{1}{\alpha }$ + $\frac{1}{\beta } )$ = $\frac{(\alpha +\beta)}{\alpha \beta}$ = $\frac{-b}{c}$

$\frac{1}{\alpha \beta } = \frac{1}{c}$

if $\frac{1}{\alpha }$ and $\frac{1}{\beta }$ are the zeroes of quadratic polynomial. then the equation is..

$x^{2}$ - $(\frac{1}{\alpha }$ + $\frac{1}{\beta } )x$ + $\frac{1}{\alpha \beta }$ = 0

$x^{2} -(\frac{-b}{c} )x + \frac{1}{c} = 0$

$x^{2} + (\frac{b}{c} )x + \frac{1}{c} = 0$

after solving this we get,

$cx^{2} +bx+1=0$

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HOPE IT HELPS YOU OUT

Answer 2

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$<b><u>PLEASE REFER TO THE ATTACHMENT FOR STEP-BY-STEP EXPLANATION.$

$\huge\mathcal[THANKS!!]$

$<marquee>hope it helps!</marquee>$