Question

$({ {x}^{2} + 5x - 2})^{2} + {x}^{2} + 5x - 7 = 0$
solve this quadratic equation fast no spam no copy paste​

Answer 1

Heya !

Question:-

• Solve the quadratic equation:- (x²+5x-2)²+x²+5x-7 = 0

Formulas to be used.

$\huge \fbox \blue{(a+b+c)²=a²+b²+c²+2ab+2bc+2ca}$

Solution:-

first let's open the bracket (x²+5x-2)² by the 1st formula.

(x²+5x-2)² = (x²)²+(5x)²+(-2)²+2(X)(5x)+2(5x)(-2)+2(-2)(X)

$\implies$ x⁴+25x²+4+10x-20x-4x

$\implies$ x⁴+25x²-14x+4

$\implies$ x⁴+25x-14x+4+x²+5x-7

$\implies$ x⁴+x²+16x-3

Since, the whole equation has the degree term of 4

it is not a Quadratic equation.

as a quadratic equation is one which has the degree term of 2, but here it's 4.

so, it's not the quadratic equation.

Answer 2

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$({ {x}^{2} + 5x - 2})^{2} + {x}^{2} + 5x - 7 = 0$

solve this quadratic equation

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Hey There!

Solution Of :-

Solve the quadratic equation:- (x²+5x-2)²+x²+5x-7 = 0

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Answer :-

No Real Solution

Given :-

Use The Quadratic Equation With

$a = 1,b = 5,c = 7 \\ \\ x = \frac{ - b + \sqrt{ {b}^{2} \: - 4ac} }{2a} \\ \\ x = \frac{ - 5 + \sqrt{(5 {)}^{2} - 4(1)(7) } }{(2)(1)} \\ \\ \\ x = \frac{ - 5 + \sqrt{25 - 28} }{2} \\ \\ x = \frac{ - 5 \sqrt{ - 3} }{2}$

∴ Answer , No Real Solution!

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