2.9.3 Quadratic Equation, SPM Practice (Paper 1)


Question 11:
The quadratic equation x 2 4x1=2p(x5) , 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 +5k6=0 has no real roots.

Solution:


Question 13:
Find the range of values of p for which the equation 5 x 2 +7x3p=6 has no real roots.

Solution:


Question 14:
Show that 6x62k x 2 = x 2  has no real roots if k> 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:




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