Chapter 5 - Quadratic Equations Exercise Ex. 5(B)

Question 1

Without solving, comment upon the nature of roots of each of the following equations :

(i)7x² - 9x +2 =0           (ii)6x² - 13x +4 =0  

 

(iii)25x² - 10x +1=0       (iv)

 

(v)x² - ax - b² =0           (vi)2x² +8x +9=0

Solution 1

 

 

Question 2 (i)

Find the value of p, if the following quadratic equation has equal roots : 4x² - (p - 2)x + 1 = 0

Solution 2 (i)

Question 2 (ii)

Find the value of 'p', if the following quadratic equations have equal roots :

x² + (p - 3)x + p = 0

Solution 2(ii)

x² + (p - 3)x + p = 0

 Here, a = 1, b = (p - 3), c = p

 Since, the roots are equal,

⇒ b²- 4ac = 0

⇒ (p - 3)²- 4(1)(p) = 0

⇒p² + 9 - 6p - 4p = 0

⇒ p²- 10p + 9 = 0

⇒p²-9p - p + 9 = 0

⇒p(p - 9) - 1(p - 9) = 0

⇒ (p -9)(p - 1) = 0

⇒ p - 9 = 0 or p - 1 = 0

⇒ p = 9 or p = 1

Question 3

The equation 3x² - 12x + (n - 5)=0 has equal roots. Find the value of n.

Solution 3

Question 4

Find the value of m, if the following equation has equal roots : (m - 2)x² - (5+m)x +16 =0

Solution 4

Question 5

Find the value of k for which the equation 3x²- 6x + k = 0 has distinct and real roots.

Solution 5