Math, asked by pratikpradeep, 1 year ago

7th answer pls for 50 points.

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pratikpradeep: find the other zeroes of the polynomial x^4-5x^3+2x^2+10x-8 if it is given that two of its zeroes are -root 2 and root 2

pratikpradeep: x is the letter not the multiplication sign

DU4ever: give me 5min ok

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Answers

Answered by HelpingHand

We know that $\sqrt{2}$ and - $\sqrt{2}$ are it's zeroes.
Hence,
$(x+ \sqrt{2})(x- \sqrt{2})$ is a factor.
We can get the other by dividing given polynomial by this one.
= $\frac{ x^{4}-5 x^{3}+2 x^{2} +10x-8 }{(x+ \sqrt{2})(x- \sqrt{2}) } \\ \\ \frac{x^{4}-5 x^{3}+2 x^{2} +10x-8 }{ x^{2} -2}$
Solving this, we get:
$x^{2} -5x+4 \\ \\ x^{2} -x-4x+4 \\ \\ x(x-1)-4(x-1) \\ \\ (x-4)(x-1) \\ \\$
x=4 or x=1

The other zeroes are: 4 and 1

HelpingHand: If you don't get the division part tell me I'll modify the answer.

Answered by poojan

Please click on the attachment given below to see the complete solution..

Hope it helps you..

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