English Medium कक्षा १० - CBSE Question Bank Solutions

If x = −2 is a root of the equation 3x² + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x² + k(4x + k − 1) + p = 0 are equal.

The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.

If 1 is a root of the quadratic equation 3x² + ax – 2 = 0 and the quadratic equation a(x² + 6x) – b = 0 has equal roots, find the value of b ?

The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?

Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?

Find the value(s) of k so that the quadratic equation 3x² − 2kx + 12 = 0 has equal roots ?

The Sum of first five multiples of 3 is ______.

If the common differences of an A.P. is 3, then a₂₀ − a₁₅ is 

Find the A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40.

The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?

Find the roots of the equation  .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, then α² + β² + γ² =

If α, β, γ are are the zeros of the polynomial f(x) = x³ − px² + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]

If α, β are the zeros of the polynomial f(x) = ax² + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]

If two of the zeros of the cubic polynomial ax³ + bx² + cx + d are each equal to zero, then the third zero is

If two zeros x³ + x² − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is

The product of the zeros of x³ + 4x² + x − 6 is

What should be added to the polynomial x² − 5x + 4, so that 3 is the zero of the resulting polynomial?