English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

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 ______.

The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.

The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure is ______.

A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle is ______.

If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.