If one root of x^{2}-5x+6=0 is also the root | vedclass

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

Question

(B) First,solve the quadratic equation $x^{2}-5x+6=0$.Factorizing the equation: $(x-2)(x-3)=0$.Thus,the roots are $x=2$ or $x=3$.Case $1$: If $x=2$ is

Vedclass · Accepted Answer

$-10$ or $-18$

Vedclass · Answer

(B) First,solve the quadratic equation $x^{2}-5x+6=0$.Factorizing the equation: $(x-2)(x-3)=0$.Thus,the roots are $x=2$ or $x=3$.Case $1$: If $x=2$ is a root of $x^{2}+3x+c=0$,then $(2)^{2}+3(2)+c=0$.$4+6+c=0 \implies 10+c=0 \implies c=-10$.Case $2$: If $x=3$ is a root of $x^{2}+3x+c=0$,then $(3)^{2}+3(3)+c=0$.$9+9+c=0 \implies 18+c=0 \implies c=-18$.Therefore,the possible values for $c$ are $-10$ or $-18$.

If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

Similar Questions

If $64$ is the discriminant of $k x^{2}-4 x-4=0$,then the value of $k$ is ...........

The sum of a natural number and its reciprocal is $\frac{5}{2}$. Then the number is $\ldots \ldots .$

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $5x^{2} - 4\sqrt{5}x + 4 = 0$.

The difference between the lengths of the sides of a right triangle which form the right angle is $7 \, cm$. If its perimeter is $30 \, cm$,find the lengths of the sides.

Obtain the roots of the following quadratic equation by using the quadratic formula: $p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module