POLYNOMIALS 1

1. If p(x) = ax² + bx + c, then −𝑏/𝑎 is equal to

2. If the square of the difference of the zeroes of the quadratic polynomial x² + px + 45 is equal to 144, find the value of p.

3. If the sum of the zeroes of the quadratic polynomial ky² + 2y – 3k is equal to twice their product, find the value of k.

4. If 𝛼,𝛽 are zeroes of the polynomial f(x) = x² – p(x + 1) – c, then find the value of (𝛼 + 1) ( 𝛽 + 1).

5. In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as :

Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.

Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the x- axis.

6. Twice the product of the zeroes of the polynomial 23x² − 26x + 161 = 14p. Find p.

7. Find the number of zeroes of the polynomial from the graph given below

8. If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then

9. If one zero of the quadratic polynomial 4x² – 8kx + 8x – 9 is negative of the other, then find the product of zeroes of kx² + 3kx + 2

10. Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion (A): Both zeroes of the quadratic polynomial x² – 2kx + 2 are equal in magnitude but opposite in sign then value of k is ½.
Reason (R): Sum of zeroes of a quadratic polynomial ax² + bx + c is -b/a.