Page 13 - CHAPTER 4 (Quadratic equations)

CHAPTER 4
QUADRATIC EQUATIONS

Checkpoint - 3

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1. The value of k(k>0) for which the equations x +kx+64=0 and x -
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8x+k=0 both will have real roots is:

2. Find the integral values of a for which the quadratic equation (x-

a)(x-10)+1=0 has equal roots.

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3. Determine the nature of the roots of the equation 3x +7x+8=0.
4. Find the values of k for which the following quadratic equation, so

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that they have real and equal roots: 9x +8kx+16=0.
5. Find the set of values of k for which the equation kx +2x+1=0 has
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distinct real roots.

E. Practical Problems:

Example 1 : The difference of two given numbers is 3, and their product
is 504. Find the numbers.

Solution: Let the required number b x and (x – 3). Then, x(x – 3) = 504

⇒ x²-3x-504=0 ⇒x²-24x+21x-504=0

⇒x(x-24)+ 21 (x-24)= 0 ⇒(x-24)(x+21)= 0

⇒x-24=0 or x+21=0 ⇒x=24 or x= -21

If x= -21, then the numbers are –21 and –24.

If x=24, then numbers are 24, 21.

So, the numbers are –21, –24 or 24, 21

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