

InterviewSolution
1. |
Determine the nature of the roots of the following quadratic equations:(i) \(2x^2-3x+5=0\)(ii) \(2x^2-6x+3=0\)(iii) \(\frac{3}{5}x^2-\frac{2}{3}x+1=0\)(iv) \(3x^2-4\sqrt{3}x+4=0\)(v) \(3x^2-2\sqrt{6}x+2=0\) |
Answer» (i) \(2x^2-3x+5=0\) For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D < 0, roots are not real If D > 0, roots are real and unequal If D = 0, roots are real and equal \(2x^2-3x+5=0\) ⇒ D = 9 – 4 × 5 × 2 = -31 Roots are not real. (ii) \(2x^2-6x+3=0\) For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D < 0, roots are not real If D > 0, roots are real and unequal If D = 0, roots are real and equal \(2x^2-6x+3=0\) ⇒ D = 36 – 4 × 2 × 3 = 12 Roots are real and distinct. (iii) \(\frac{3}{5}x^2-\frac{2}{3}x+1=0\) For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D < 0, roots are not real If D > 0, roots are real and unequal If D = 0, roots are real and equal \(\frac{3}{5}x^2-\frac{2}{3}x+1=0\) ⇒ D = 4/9 – 4 × 3/5 × 1 = -88/45 Roots are not real. (iv) \(3x^2-4\sqrt{3}x+4=0\) For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D < 0, roots are not real If D > 0, roots are real and unequal If D = 0, roots are real and equal \(3x^2-4\sqrt{3}x+4=0\) ⇒ D = 48 – 4 × 3 × 4 = 0 Roots are real and equal (v) \(3x^2-2\sqrt{6}x+2=0\) For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D < 0, roots are not real If D > 0, roots are real and unequal If D = 0, roots are real and equal \(3x^2-2\sqrt{6}x+2=0\) ⇒ D = 24 – 4 × 3 × 2 = 0 Roots are real and equal. |
|