## CBSE 10 Math Practice Paper 02

### Polynomials

1. Find the zeroes of the quadratic polynomial \(x^2+7x+10\) and verify the relation between the zeroes and the coefficients.

2. Verify that \(3, -1, \frac{1}3\) are the zeroes of the cubic polynomial \(p(x)=3x^2-5x-11x-3\) and then verify the relationship between the zeroes and the coefficients.

3. Find all the zeroes of \(2x^4-3x^3-3x^2+6x-2\), if two of its zeroes are \(\sqrt2\) and - \(\sqrt2\).

4. If two zeroes of the polynomial \(x^4-6x^3-26x^2+138x\) are 2 + \(\sqrt3\) and 2 - \(\sqrt3\), find the other zeroes.

5. If the zeroes of the polynomial \(x^3-3x^2+x+1\) are \(a - b, a, a + b\) , find `a' and 'b`.

6. For what value of k, (–4) is a zero of the polynomial \(x^2 – x – (2k + 2)\)?

7. Find the zeroes of the polynomial \(x^2 – x – 6\).

8. Write a quadratic polynomial, the sum and product of whose zeroes are 3 and –2 respectively.

9. If α and β are zeroes of the quadratic polynomial \(x^2 – 6x + a\) find the value of \(a\) if \(3α + 2β = 20\).

10. If the polynomial \(x^4 + 2x^3 + 8x^2 + 12x + 18\) is divided by another polynomial \( x^2 + 5\), the remainder comes out to be \(px + q\). Find the value of p and q.

11. Find the quadratic polynomial if its zeroes are 0, \(\sqrt5\).

12. If \(α, β \) are the zeros of the polynomial, such that \(α+β=6\) and \(α- β=8\), then write the polynomial.

13. If \(\alpha\) and \(β\) are zeros of \(6x^2 + 10x + 26\), then find the value of \(\frac{1}α + \frac{1}β\).

14. Find p and q if p and q are the zeros of the quadratic polynomial \(px^2+ x + q\).

15. Find the zeroes of the quadratic polynomial \(x^2 + 99x + 127\).