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If alpha and beta are the zeros of the p...

If `alpha` and `beta` are the zeros of the polynomial `f(x)=x^2+p x+q`, form a polynomial whose zeros are `(alpha+beta)^2` and `(alpha-beta)^2`.

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To form a polynomial whose zeros are \((\alpha + \beta)^2\) and \((\alpha - \beta)^2\), we can follow these steps: ### Step 1: Identify the values of \(\alpha + \beta\) and \(\alpha \beta\) From the polynomial \(f(x) = x^2 + px + q\), we know: - The sum of the roots (zeros) \(\alpha + \beta = -\frac{p}{1} = -p\) (using Vieta's formulas). - The product of the roots \(\alpha \beta = \frac{q}{1} = q\). ### Step 2: Calculate \((\alpha + \beta)^2\) ...
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RD SHARMA-POLYNOMIAL-All Questions
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  2. Draw the graph of the quadratic polynomial f(x)=3-2x-x=2

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  3. If alpha and beta are the zeros of the polynomial f(x)=x^2+p x+q, form...

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  4. Draw the graph of the polynomial f(x)=-42+4x-1. Also find the vertex o...

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  5. If the sum of the zeros of the quadratic polynomial f(t)=k t^2+2t+3k i...

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  6. Draw the graph of the polynomial f(x)=-3x^2+x.

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  7. Find the zeros of the quadratic polynomial x^2+7x+12 , and verify the ...

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  8. Find the zeros of polynomial f(x) = 4sqrt3 x^2 + 5x - 2sqrt 3; and ver...

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  9. If alpha and beta are the zeros of the quadratic polynomial f(x)=x^2-p...

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  10. Obtain all the zeros of the polynomial f(x)=3x^4+6x^3−2x^2−10x−5, if ...

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  11. What must be subtracted from 8x^4+14 x^3-2x^2+7x-8 so that the resulti...

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  12. By applying division algorithm prove that the polynomial g(x)=x^2+3x+1...

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  13. Find the condition that the zeroes of the polynomial f(x) = x^3 – px^2...

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  14. Find the zeros of the polynomial f(x)=x^3-5x^2-2x+24 , if it is given ...

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  15. Draw the graph of the polynomial f(x)=x2-6x=9.

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  16. If alphaa n dbeta are the zeros of the quadratic polynomial f(x)=x^2-...

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  17. Draw the graph of the polynomial f(x)=x^3-4x .

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  18. Draw the graph of the cubic polynomial f(x)=x^3-2x^2 .

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  19. Draw the graph of the polynomial f(x)=x^3 .

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  20. If each one of the following graphs is the graph of a polynomial, then...

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