Page 12 - CHAPTER 4 (Quadratic equations)

CHAPTER 4

QUADRATIC EQUATIONS

Now, by quadratic formula, x= -b±√D = 6±√12 = 6±2√3 = 3±√3
2a 2 ×2 4 2

Hence the roots are x= 3+√3 , 3-√3
2 2

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(ii). Here, the given equation is 2x -3x+5=0;
Comparing it with ax²+bx+c=0, we get

A = 2, b = –3 and c = 5

∴ Discriminant, D = b² – 4ac = 9 – 4 x 2 x 5 = 9 – 40 = –31

∵ D<0, the equation has no real roots.

Example 10:

Find the value of k for the following quadratic equation so that its

roots are real and equal. 9 ² + 8 + 16 = 0.

Solution:

The given equation 9x²+8kx+16=0

Comparing it with ax²+bx+c=0, we get

a = 9, b = 8k and c = 16.

∴ Discriminant, D = b² – 4ac = (8k)² – 4 x 9 x 16 = 64k² – 576

Since roots are real and equal, so

D = 0 ⇒ 64k² – 576 = 0 ⇒ 64k² = 576

⇒ k² = 576 = 9 ⇒ k = ± 3
64

Hence, k = 3, –3

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