2.12.5 Quadratic Functions, SPM Practice (Paper 1)


Question 13:
Show that 6x62k x 2 = x 2  has no real roots if k> 1 4 .

Solution:



Question 14:
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:






Question 15:
The straight line y = 5x – 1 does not intersect with the curve y = 2x2 + x + h.
Find the range of values of h.

Solution:
y=5x1  …… (1) y=2 x 2 +x+h …… (2) Substitute (1) into (2), 5x1=2 x 2 +x+h 2 x 2 +x+h5x+1=0 2 x 2 4x+h+1=0   b 2 4ac<0 ( 4 ) 2 4( 2 )( h+1 )<0  168h8<0 8<8h h>1

Question 16:
Find the range of values of p for which the equation 2 x 2 +5x+3p=0 has two real distinct roots.

Solution:

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