List of top Mathematics Questions on Basic Algebra

Solution of \( \frac{x^2 - 4x + 7}{x^2 - 7x + 12} \le \frac{2}{3} \) is/are:
Choose the correct answer:

If the sum of the zeroes of the polynomial (p(x)=2x^3-3kx^2+4x-5) is 6, then the value of k is

In an arithmetic progression, the sum of the first 10 terms is 210 and the sum of the next 10 terms is 610. What is the common difference of the arithmetic progression?

Find the value of the following algebraic expression: \[ \frac{(0.64)^{3}-(0.36)^{3}}{(0.64)^{2}+(0.64)(0.36)+(0.36)^{2}} = \]

If () and () are the roots of the quadratic equation (2x^2-3x-1=0), then find the value of (^4+^4).

If (_2128=a), (_3813=b), then (a-2b=)

Match the following:

If \(p(x) = 4x^{11} - 8x^9 + 7x^5 + 6x^3 + 4x^2 + 5x + 6\), then the number of zeros is ________.

For \((k \neq 0)\), if the quadratic equation \(kx(x - 2) + 6 = 0\) has two equal roots, then find the value of \(k\).

If \[ \frac{3}{x + y} + \frac{12}{2x - y} = \frac{7}{3} \text{ and } \frac{6}{x + y} + \frac{18}{2x - y} = \frac{11}{3}, \text{ then } x^2 + y^2 = \]

The roots of the equation \( x^4 - 5x^2 + 4 = 0 \) are

If \(\log{\left(\frac{x+y}{3}\right)} = \frac{1}{2} \left(\log{x} + \log{y}\right)\) then the value of \(\frac{x}{y} + \frac{y}{x}\) is?