Question

6. Write the discriminant of quadratic equation: (x + 5)2 = 2 (5x - 3).
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Answer 1

Given :-

(x + 5)² = 2(5x-3)

To find :-

Discriminant of Quadratic equation

Solution:-

First lets simplify the equation

(x + 5)² = 2(5x-3)

In LHS it is in form of (a+b)² = a²+ 2ab + b²

(x + 5)² = 2(5x-3)

x² + 2(x)(5) + (5)² = 10x - 6

x² + 10x + 25 = 10x - 6

Transpose all terms to LHS

x² + 10x + 25 - 10x + 6 = 0

x² + 10x - 10x + 25 + 6 = 0

x² + 0x + 31 = 0

Hence, It is a Quadratic equation

Discriminant of Quadratic equation is b²- 4ac

x² + 0x + 31 = 0

• a = 1
• b = 0
• c = 31

D= (0)² - 4(1)(31)

D = 0- 124

D = -124

Hence Discriminant of (x + 5)² = 2(5x-3) is -124

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Know more :-

Discriminant is denoted by D or Δ

• Discriminant helps to find the nature of roots

Thereare some cases to find the nature of roots

• D=0 Roots are real & equal
• D>0 Roots are Real &Distinct roots
• D<0 Roots are Complex & Conjugate to each other
• D>0 and Perfect square Roots are Rational and Real
• D<0 and not perfect square Roots are Irrational and Real