Quadratic Equations Quiz 16

If the equation $\frac{x^2-bx}{ax-c}=\frac{m-1}{m+1}$ has roots which are numerically equal but of opposite sign, then the value of ‘m’ must be

Two consecutive positive integers differ by

The sum of a number and its reciprocal is $\frac{5}{2}$. Represent this, situation in the form of a quadratic equation.

Two consecutive even integers are

Two consecutive positive integers are

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each and the product of the number of marbles they have now is 124. Represent this situation in the form of quadratic equation.

What is the condition that one root of the quadratic equation $ax^2+bx+c=0$ is reciprocal of the other ?

If the roots of the quadratic equation $ax^2+bx+c=0$ are $sin\;\alpha$ and $cos\;\alpha,$ then

If the difference of the roots of the quadratic equation $x^2-ax+b=0$ is 1, then

The value of c for which the equation $ax^2+bx+c=0$ has equal roots is