Simplification-Practice test
If (x-k) is a common factor of the equations 4x2– 9x + 5 = 0 and (p-1) x2 – 3x-1 = 0 and k <= 1, then find the value of p.
If (x-k) is a factor of 4x2 – 9x + 5 = 0
4k2-9k + 5 = 0 –> k = 5/4, 1
As k <= 1 k = 1
As k is also a factor of
(p-1)x2 – 3x – 1 = 0 –>(p-1)k2-3k-1 = 0
–> (p-1) 12-3-1 = 0 –> p = 5
The sum and the product of the roots of the quantratic equation x2 + 20x + 3 = 0 is
Given equation is x2 + 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
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 x2 + (2a + 3)x + (5-a) = 0 has both the roots as real and negative, then what is the greatest positive integral value of a?
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