The roots of a²x² + abx = b², are :

Important Questions on Theory of Equations

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 18

Determine the value of k for which the quadratic equation 4x² - 3kx + 1 = 0 has equal roots :

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 20

Find the value of $k$ so that the sum of the roots of the quadratic equation is equal to the product of the roots $(k+1)x^2+2kx+4=0$?

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 21

If $-4$ is a root of the quadratic equation ${\mathrm{x}}^2-\mathrm{px}-4=0$ and the quadratic equation ${\mathrm{x}}^2-\mathrm{px}+\mathrm{k}=0$ has equal roots, find the value of $\mathrm{k}$ :

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 23

Find the value of p for which the quadratic equation x² + p (4x + p - 1) + 2 = 0 has equal roots :

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 32

If $\alpha ,\beta$ are the roots of the equation $3x^2-6x+4=0$, find the value of $\left(\frac{{\alpha }^2}{\beta }+\frac{{\beta }^2}{\alpha }\right)+\left(\frac{\alpha }{\beta }+\frac{\beta }{\alpha }\right)+2\left(\frac{1}{\alpha }+\frac{1}{\beta }\right)+3\alpha \beta$

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 35

The length of the hypotenuse of a right triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm.Find the length of each side of the triangle.

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 36

A two digit number is such that the product of its digits is $12.$ When $9$ is addded to the number, the digits interchange their places, find the number:

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 37

A plane left $40$ minutes late due to bad weather and in order to reach its destination, $1600 \mathrm{km}$ away in time, it had to increase its speed by $400 \mathrm{km}/\mathrm{hr}$ from its usual speed. Find the usual speed of the plane.