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Find the quadratic polynomial whose zeros …

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Find the quadratic polynomial whose zeros are 2/3 and -1/4 . Verify the relation between the Coefficient And the zeros of the polynomial

Posted by Jasmine Ghosh 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

The polynomial with α and β as roots is:

f(x)=x²-(α+β)x+αβ
x²-{tex}(\frac 23-\frac 14){/tex}x+{tex}(\frac 23)(-\frac 14){/tex}

{tex}\mathrm x^2-\frac5{12}\mathrm x-\frac16{/tex}

or f(x)=12x²-5x-2

here a=12,b=-5,c=-2
Sum of zeros = {tex}\frac23-\frac14=\frac5{12}=-\frac{\mathrm b}{\mathrm a}{/tex}
Product of zeros = {tex}\frac23\times-\frac14=-\frac16=\frac{-2}{12}=\frac{\mathrm c}{\mathrm a}{/tex}
Hence relation of coefficients and zeros is verified

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CBSE > Class 10 > Mathematics