JIPMAT Algebra > Quadratic Equations PYQs

Amit and Alok attempted to solve a quadratic equation. Amit made a mistake in writing down the constant term and ended up with roots $(4, 3)$. Alok made a mistake in writing down coefficient of $x$ to get roots $(3, 2)$. The correct roots of the equation are:

If the roots of the equation $x^{2}-p x+54=0$ are in the ratio $2: 3$, then value of $p$ is:

If $\alpha$ and $\beta$ are the roots of the equation $a x^{2}+b x+c=0$, then value of $\frac{1}{a \alpha+b}+\frac{1}{a \beta+b}$ is :

The factors of polynomial $x^{3}-6 x^{2}+11 x-6$ are :

If highest common factor of $x^{2}-p x-q$ and $5 x^{2}-3 p x-15 q$ is $(x-3)$, then value of ( $\left.p, q\right)$ will be :

The graph of a polynomial $y = f(x)$ is shown in figure below, then the number of its zeros is: <img src="https://balti.afterboards.in/bKbZmXAxDAlKPRR" width=300px>

<p>Given below are two statements:</p><p>Statement (I): (x² + 3x + 1) = (x - 2)² is not a quadratic equation.</p><p>Statement (II): The nature of roots of quadratic equations x² + 2x√3 + 3 = 0 are real and equal.</p><p>In light of the above statements, choose the most appropriate answer from the options given below.</p>

If $\sin (\alpha)$ and $\cos (\alpha)$ are the roots of the equation $a x^{2}+b x+c=0$, then $b^{2}$ is