If (x-k) is a common factor of the equations 4x^{2}– 9x + 5 = 0 and (p-1) x^{2} – 3x-1 = 0 and k <= 1, then find the value of p.

**Answer:**Option C

**Explanation:**

If (x-k) is a factor of 4x^{2} – 9x + 5 = 0

4k^{2}-9k + 5 = 0 –> k = 5/4, 1

As k <= 1 k = 1

As k is also a factor of

(p-1)x^{2} – 3x – 1 = 0 –>(p-1)k^{2}-3k-1 = 0

–> (p-1) 1^{2}-3-1 = 0 –> p = 5

The sum and the product of the roots of the quantratic equation x^{2} + 20x + 3 = 0 is

**Answer:**Option D

**Explanation:**

Given equation is x^{2} + 20x + 3 = 0 —-(1)

Comparing (1) with general form of quantratic equation (1) in option 4, sum of the roots and the product of the roots are -20 and 3 respectively.

If 1.5x=0.04y then the value of (y-x)/(y+x) is

**Answer:**Option B

**Explanation:**

x/y = 0.04/1.5 = 2/75

So (y-x)/(y+x) = (1 – x/y)/(1 + x/y) = (1 – 2/75)/ (1 + 2/75) = 73/77.

If x^{2 }+ (2a + 3)x + (5-a) = 0 has both the roots as real and negative, then what is the greatest positive integral value of a?

**Answer:**Option D

**Explanation:**

Since both the roots are negative, Sum of the roots is negative and product of the roots is positive.

2a + 3 < 0 –> a > -3/2.

Also, 5 – a > 0 –> a < 5

Greatest possible integer value of a = 4