If one of the roots of the equation {x^2} + a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given,$3$ is a root of the equation ${x^2} + ax + 3 = 0$.Substituting $x = 3$ into the equation: ${3^2} + a(3) + 3 = 0$.$9 + 3a + 3 = 0$ implies $

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Given,$3$ is a root of the equation ${x^2} + ax + 3 = 0$.Substituting $x = 3$ into the equation: ${3^2} + a(3) + 3 = 0$.$9 + 3a + 3 = 0$ implies $3a = -12$,so $a = -4$.Now,consider the equation ${x^2} + ax + b = 0$. Substituting $a = -4$,we get ${x^2} - 4x + b = 0$.Let the roots of this equation be $\alpha$ and $3\alpha$ (since one root is three times the other).From the sum of roots formula,$\alpha + 3\alpha = -(-4)/1 = 4$.$4\alpha = 4$,which gives $\alpha = 1$.The roots are $1$ and $3(1) = 3$.From the product of roots formula,$\alpha \cdot 3\alpha = b/1$.$1 \cdot 3 = b$,so $b = 3$.

If one of the roots of the equation ${x^2} + ax + 3 = 0$ is $3$ and one of the roots of the equation ${x^2} + ax + b = 0$ is three times the other root,then the value of $b$ is equal to

Similar Questions

The value of $a$ for which one root of the quadratic equation $(a^2 - 5a + 3)x^2 + (3a - 1)x + 2 = 0$ is twice as large as the other,is

Solve the given two equations and select the correct answer from the given options.
$I. x^{2} + 12x + 32 = 0$
$II. 2y^{2} + 15y + 27 = 0$

The number of real solutions of the equation $|x|^2 - 3|x| + 2 = 0$ is:

If $3 + 4i$ is a root of the equation ${x^2} + px + q = 0$ ($p, q$ are real numbers),then

The quadratic equation with rational coefficients,whose one root is $\sqrt{5}$,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module