2.9.3 Quadratic Equation, SPM Practice (Paper 1)

Question 11:
The quadratic equation $x^2-4x-1=2p(x-5)$ , where p is a constant, has two equal roots. Calculate the possible values of p.

Solution:

Question 12:
Find the range of values of k for which the equation $x^2-2kx+k^2+5k-6=0$ has no real roots.

Solution:

Question 13:
Find the range of values of p for which the equation $5x^2+7x-3p=6$ has no real roots.

Solution:

Question 14:
$\text{Show that }6x-6-2k{x}^2=x^2\text{ has no real roots if }k>\frac{1}{4}.$

Solution:

Question 15:
The quadratic equation $x^2+px+q=0$ has roots –2 and 6. Find
(a) the value of p and of q,
(b) the range of values of r for which the equation $x^2+px+q=r$ has no real roots.

Solution: