CBSE Class 10 Answered
Let alpha and beta are the zeroes of a quadratic polynomial 2x²-5x-6 then form a quadratic polynomial whose zeroes are alpha+beta and alpha×beta
Asked by geetayadav18081983 | 15 Jun, 2022, 13:19: PM
Given quadratic equation is
f(x) = 2x2 -5x - 6
roots of above quadratic equation are
and ![begin mathsize 14px style fraction numerator 5 minus square root of 25 minus 4 left parenthesis 2 right parenthesis left parenthesis negative 6 right parenthesis end root over denominator 2 cross times 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/909f25f2fe5aa00653a7b2fabef99dc8.png)
![begin mathsize 14px style fraction numerator 5 plus square root of 25 minus 4 left parenthesis 2 right parenthesis left parenthesis negative 6 right parenthesis end root over denominator 2 cross times 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/89cb2664876e86dcd922df4350061105.png)
![begin mathsize 14px style fraction numerator 5 minus square root of 25 minus 4 left parenthesis 2 right parenthesis left parenthesis negative 6 right parenthesis end root over denominator 2 cross times 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/909f25f2fe5aa00653a7b2fabef99dc8.png)
roots of above quadratic equation are
and ![begin mathsize 14px style fraction numerator 5 minus square root of 73 over denominator 4 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/d0f4319f66862c49aa1422150dc289ed.png)
![begin mathsize 14px style fraction numerator 5 plus square root of 73 over denominator 4 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/3f8666d065eca7f3a3422a6c83a47f52.png)
![begin mathsize 14px style fraction numerator 5 minus square root of 73 over denominator 4 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/d0f4319f66862c49aa1422150dc289ed.png)
Hence
and ![begin mathsize 14px style beta space equals space fraction numerator 5 minus square root of 73 over denominator 4 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/15a431f1d1ea7f16c08f8355a16e1674.png)
![begin mathsize 14px style alpha space equals space fraction numerator 5 plus square root of 73 over denominator 4 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/05cb175be508a36892492f9e9519ca24.png)
![begin mathsize 14px style beta space equals space fraction numerator 5 minus square root of 73 over denominator 4 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/15a431f1d1ea7f16c08f8355a16e1674.png)
If roots of a quadratic equition are (α + β ) and ( α β ) , then quadratic equation is
g(x) = x2 - (α + β + α β ) x + (α + β ) ( α β )
![begin mathsize 14px style alpha space plus beta equals space fraction numerator 5 plus square root of 73 over denominator 4 end fraction plus fraction numerator 5 minus square root of 73 over denominator 4 end fraction space equals space 5 over 2 end style](https://images.topperlearning.com/topper/tinymce/cache/404e6429a5ca1bde5ae62b8912b05013.png)
![begin mathsize 14px style alpha space beta space equals space open parentheses space fraction numerator 5 plus square root of 73 over denominator 4 end fraction space close parentheses space space stretchy left parenthesis space fraction numerator 5 minus square root of 73 over denominator 4 end fraction space stretchy right parenthesis space equals space 1 over 16 open parentheses 25 plus 73 minus 10 square root of 73 close parentheses space equals 49 over 8 minus 5 over 8 square root of 73 end style](https://images.topperlearning.com/topper/tinymce/cache/01971ba624edb2c08406c9a06231d527.png)
Hence quadratic equation is
![begin mathsize 14px style g left parenthesis x right parenthesis space equals space x squared space minus space open parentheses 5 over 2 space plus space 49 over 8 space minus space 5 over 8 square root of 73 close parentheses x space plus 5 over 16 open parentheses 49 minus 5 square root of 73 close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/298b94fdd7d0596d8607a7e8969925cb.png)
![begin mathsize 14px style g left parenthesis x right parenthesis space equals space x squared space minus space open parentheses space 69 over 8 space minus space 5 over 8 square root of 73 close parentheses x space plus 5 over 16 open parentheses 49 minus 5 square root of 73 close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/fcd97671b9612e78af48d1fe1af6bf14.png)
![begin mathsize 14px style g left parenthesis x right parenthesis space equals space 16 space x squared space minus space open parentheses space 138 space minus space 10 square root of 73 close parentheses x space plus open parentheses 245 minus 25 square root of 73 close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/5c2914f8f4a55978f55fb894b05ad495.png)
Answered by Thiyagarajan K | 15 Jun, 2022, 14:43: PM
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