Question

solve the quadratic equation by using quadratic formula x2 - 7 x + 18 =0

Answer 1

Roots of the quadratic equation x²-7x+18=0 are complex and shown below:

$\bf x_{1} = \frac{7+ i \sqrt{23} }{2}$

$\bf x_{2} = \frac{7 - i \sqrt{23} }{2}$

Given:

• ${x}^{2}-7x+18 = 0$

To find:

• Find the solution of the equation.

Solution:

Standard Quadratic equation is given by $a {x}^{2} + bx + c = 0$

So,Quadratic formula

$\bf x_{1,2}= \frac{- b \pm \sqrt{ {b}^{2} -4 ac} }{2a}$

Here, in the given equation

${x}^{2} - 7x + 18 = 0$

$a = 1 \\ b = - 7 \\ c = 18$

$x_{1,2} = \frac{7 \pm \sqrt{49 - 72} }{2}$

$x_{1,2} = \frac{7 \pm \sqrt{ - 23} }{2}$

$\bf x_{1} = \frac{7+ i \sqrt{23} }{2}$

$\bf x_{2} = \frac{7- i \sqrt{23} }{2}$

Hence equation has complex roots.

No real roots exist for the given Quadratic equation.

Hope it helps you.

Answer 2

solve the quadratic equation by using quadratic formula x2 - 7 x + 18 =0

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