English Medium कक्षा १० - CBSE Question Bank Solutions

10. The zeroes of the quadratic polynomial x² + kx + k, k? 0.

If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then ______.

If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.

A quadratic polynomial, whose zeores are -4 and -5, is ______.

The zeroes of the quadratic polynomial x² + 1750x + 175000 are ______.

If x³ + 1 is divided by x² + 5, then the possible degree of quotient is ______.

If x³ + 11 is divided by x² – 3, then the possible degree of remainder is ______.

If x⁴ + 3x² + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are ______.

If one of the zeroes of the cubic polynomial x³ + px² + qx + r is -1, then the product of the other two zeroes is ______.

If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as ______.

If one of the zeroes of the quadratic polynomial (k -1)x² + kx + 1 the value of k is ______.

A polynomial of degree n has ______.

Consider the following statements.

1. x – 2 is a factor of x³ – 3x² + 4x – 4.
2. x + 1 is a factor of 2x³ + 4x + 6.
3. x – 1 is a factor of x⁵ + x⁴ – x³ + x² -x + 1.

In these statements

If f(x) = 5x - 10 is divided by x – `sqrt2`, then the remainder will be ______.

If 4x² – 6x – m is divisible by x – 3, the value of m is exact divisor of ______.

The number of polynomials having zeroes as -2 and 5 is ______.

The distance between the points A(0, 6) and B(0, -2) is ______.

The distance between the points (0, 5) and (–5, 0) is ______.

AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.

The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.