Question

If one of the roots of the quadratic equation 2x2 - 7x + q = 0 is 3, find the other root.

Answer 1

Step-by-step explanation:

18-7(3)+q=0

q-3=0

q=3

2x^2-7x+3=0

2x^2-6x-x+3=0

2x(x-3) -1(x-3) =0

x=3, x=1/2

Answer 2

The other root is $\frac{1}{2}$.

Step-by-step explanation:

Given : If one of the roots of the quadratic equation $2x^2-7x+q=0$ is 3.

To find : The other root ?

Solution :

If 3 is the root of the quadratic equation $2x^2-7x+q=0$ then it satisfy the equation.

$2(3)^2-7(3)+q=0$

$18-21+q=0$

$-3+q=0$

$q=3$

The equation became $2x^2-7x+3=0$

Solving by quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=2, b=-7 and c=3

$x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)}}{2(2)}$

$x=\frac{7\pm\sqrt{25}}{4}$

$x=\frac{7\pm5}{4}$

$x=\frac{7+5}{4},\frac{7-5}{4}$

$x=3,0.5$

Therefore, the other root is $\frac{1}{2}$.

#Learn more

If one root of a quadratic polynomial is 3 minus root 8 then find the quadratic polynomial.

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