Question

find the roots of quadractic equation x²-4x-21=0 by formula method​

Answer 1

Answer:

equation:

x^2-4x-21=0

x^2-7x+3x-21=0 (by splitting middle term)

x(x-7)+3(x-7)=0

(x+3) (x-7)=0

*x+3=0

x= -3

*x-7=0

x=7

therefore the required roots of the above equation are -3 and 7.

(i hope it will help u in excellent understanding)

Answer 2

✭ Solution

P(x) = ax² + bx + c = 0

The given Quadratic equation is : -

→ x²-4x-21=0

Formula

$x = \dfrac{ -b± \sqrt{ {b}^{2} - 4ac } }{2a}$

Where ,

x are the roots of the quadratic equation and

a , b , c are the coefficients of the unknown terms.

Here a = 1 , b = -4 , c = -21

By substituting the values in the formula ,

$x = \dfrac{4± \sqrt{ {( - 4)}^{2} + 84 } }{2}$

$x = \dfrac{4± \sqrt{16 + 84} }{2}$

$x = \dfrac{4± \sqrt{100} }{2}$

$x = \dfrac{4±10}{2}$

$x = \frac{4 + 10}{2} , \: \frac{4 - 10}{2}$

$x = \frac{14}{2} , \frac{ - 6}{2}$

$\bf \: \: \therefore \: x = 7, - 3$

Hence the roots of the equation are 7 , - 3 respectively.

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