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

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(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 $-18$

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(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 $c = \ldots$

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