2.9 Quadratic Equation, SPM Practice (Paper 1)


Question 6:
Write and simplify the equation whose roots are the reciprocals of the roots of 3 x 2 +2x1=0 , without solving the given equation.

Solution:


Question 7:
Find the value of p if one root of x 2 +px+8=0 is the square of the other.

Solution:


Question 8:
If one root of 2 x 2 +px+9=0 is twice the other, find the values of p.

Solution:


Question 9:
The roots of the equation 6 x 2 +hx+1=0 are α and β, whereas 3α and 3β are the roots of the equation 2 x 2 x+k=0 . Find the value of h and k.

Solution:
6 x 2 +hx+1=0 a=6, b=h, c=1 Roots=α,β sor: α+β= b a α+β= h 6 ………( 1 ) por: αβ= c a αβ= 1 6 ………( 2 ) 2 x 2 x+k=0 a=2, b=1, c=k Roots=3α, 3β sor: 3α+3β= b a 3( α+β )= ( 1 ) 2 α+β= 1 6 ………( 3 ) por: 3α( 3β )= c a 9αβ= k 2 k=18αβ………( 4 ) Substitute ( 3 ) into ( 1 ) α+β= h 6 1 6 = h 6 h=1 Substitute ( 2 ) into ( 4 ) k=18αβ k=18( 1 6 ) k=3



Question 10:
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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