Sum of the roots

Algebra Level 2

Find the sum of the roots of the quadratic equation 7 x 2 + 3 x − 4 = 0 7x^2+3x-4=0 .

3 7 \dfrac{3}{7} − 3 7 \dfrac{-3}{7} − 4 7 \dfrac{-4}{7} 4 7 \dfrac{4}{7}

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1 solution

By Vieta’s Formula

If x 1 x_1 and x 2 x_2 are the roots of the quadratic equation a x 2 + b x + c = 0 ax^2+bx+c=0 , then the sum of the roots is

x 1 + x 2 = − b a x_1+x_2=\dfrac{-b}{a}

In here our a = 7 , b = 3 a=7,b=3 and c = − 4 c=-4 , so we have

x 1 + x 2 = − 3 7 x_1+x_2=\dfrac{-3}{7}

Alternate solution: Use the quadratic formula to find the roots. Then add.

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