Question

Write the discriminant of the following quadratic equations:

(i) \(2x^2-5x+3 =0\)

(ii) \(x^2+2x+4=0\)

(iii) \((x-1)(2x-1)=0\)

(iv) \(x^2-2x+k=0,k\,ϵ\,R\)

(v) \(\sqrt{3}x^2+2\sqrt{2}x-2\sqrt{3}=0\)

(vi) \(x^2-x+1=0\)

Answer 1

(i) \(2x^2-5x+3 = 0\)

For a quadratic equation, ax² + bx + c = 0,

Discriminant, D = b² – 4ac

\(2x^2-5x+3 = 0\)

⇒ D = 25 – 4 × 2 × 3 = 1

(ii) \(x^2+2x+4=0\)

For a quadratic equation, ax² + bx + c = 0,

Discriminant, D = b² – 4ac

Given,  \(x^2+2x+4=0\)

⇒ D = 4 – 4 × 4 × 1 = - 12

(iii) \((x-1)(2x-1)=0\)

For a quadratic equation, ax² + bx + c = 0,

Discriminant, D = b² – 4ac

Given,  \((x-1)(2x-1)=0\)

⇒ 2x² – 3x + 1 = 0

⇒ D = 9 – 4 × 2 × 1 = 1

(iv) \(x^2-2x+k=0\,k\,ϵ\,R\)

For a quadratic equation, ax² + bx + c = 0,

Discriminant, D = b² – 4ac

\(x^2-2x+k=0\,k\,ϵ\,R\)

⇒ D = 4 – 4 × 1 × k = 4 – 4k

(v) \(\sqrt{3}x^2+2\sqrt{2}x-2\sqrt{3}=0\)

For a quadratic equation, ax² + bx + c = 0,

Discriminant, D = b² – 4ac

\(\sqrt{3}x^2+2\sqrt{2}x-2\sqrt{3}=0\)

⇒ D = 8 – 4 × √3 × -2√3 = 32

(vi) \(x^2-x+1=0\)

For a quadratic equation, ax² + bx + c = 0,

Discriminant, D = b² – 4ac

Given,  \(x^2-x+1=0\)

⇒ D = 1 – 4 × 1 = -3