Quadratic missing coefficient from roots Practice Questions

Warm-upeasy

Which value of $k$ makes $x^{2}+2x+k=0$ have solutions $x=-6$ and $x=4$ ?

If the zeros are $x=-6$ and $x=4$ , that means the factors of the equation are $(x+6)$ and $(x-4)$ . The product of these factors is $x^{2}+2x-24$ . Comparing with $x^{2}+2x+k$ , the missing constant is $k=-24$ .

Mid-gameeasy

For which value of $n$ does $x^{2}-7x+n=0$ have solutions $x=1$ and $x=6$ ?

If the zeros are $x=1$ and $x=6$ , that means the factors of the equation are $(x-1)$ and $(x-6)$ . The product of these factors is $x^{2}-7x+6$ . Comparing with $x^{2}-7x+n$ , the missing constant is $n=6$ .

Mid-gameeasy

Given that $x=2$ and $x=4$ are solutions of $x^{2}+mx+8=0$ , find $m$ .

If the zeros are $x=2$ and $x=4$ , that means the factors of the equation are $(x-2)$ and $(x-4)$ . The product of these factors is $x^{2}-6x+8$ . Comparing with $x^{2}+mx+8$ , the missing linear coefficient is $m=-6$ .

Mid-gamemedium

If $x=8$ and $x=-5$ are solutions of $x^{2}-3x+m=0$ , what is the value of $m$ ?

If the zeros are $x=8$ and $x=-5$ , that means the factors of the equation are $(x-8)$ and $(x+5)$ . The product of these factors is $x^{2}-3x-40$ . Comparing with $x^{2}-3x+m$ , the missing constant is $m=-40$ .

Mid-gamemedium

Find the value of $n$ so that $x^{2}+nx+12=0$ has solutions $x=-3$ and $x=-4$ .

If the zeros are $x=-3$ and $x=-4$ , that means the factors of the equation are $(x+3)$ and $(x+4)$ . The product of these factors is $x^{2}+7x+12$ . Comparing with $x^{2}+nx+12$ , the missing linear coefficient is $n=7$ .

Mid-gamemedium

The quadratic equation $x^{2}+px-18=0$ has zeros $x=9$ and $x=-2$ . What is $p$ ?

If the zeros are $x=9$ and $x=-2$ , that means the factors of the equation are $(x-9)$ and $(x+2)$ . The product of these factors is $x^{2}-7x-18$ . Comparing with $x^{2}+px-18$ , the missing linear coefficient is $p=-7$ .

Mid-gamemedium

What value of $n$ makes the solutions of $x^{2}-x+n=0$ be $x=5$ and $x=-4$ ?

If the zeros are $x=5$ and $x=-4$ , that means the factors of the equation are $(x-5)$ and $(x+4)$ . The product of these factors is $x^{2}-x-20$ . Comparing with $x^{2}-x+n$ , the missing constant is $n=-20$ .

Buzzer beatermedium

For what value of $n$ does $x^{2}+nx-10=0$ have solutions $x=-5$ and $x=2$ ?

If the zeros are $x=-5$ and $x=2$ , that means the factors of the equation are $(x+5)$ and $(x-2)$ . The product of these factors is $x^{2}+3x-10$ . Comparing with $x^{2}+nx-10$ , the missing linear coefficient is $n=3$ .

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