Question 1 :
Find the sum and the product of the roots of the following equations.
(i) x2-6x+5 = 0 Solution
(ii) kx2+rx+pk = 0 Solution
(iii) 3x2-5x = 0 Solution
(iv) 8x2-25 = 0 Solution
Question 2 :
Form a quadratic equation whose roots are
(i) 3, 4 Solution
(ii) 3+√7, 3-√7 Solution
(iii) (4+√7)/2, (4-√7)/2 Solution
Question 3 :
If α and β are the roots of the equation
3x2-5x+2 = 0
then find the values of
(i) (α/β) + (β/α)
(ii) α - β
(iii) (α²/β) + (β²/α) Solution
Question 4 :
If α and β are the roots of
3x2-6x+4 = 0
find the value of α2+β2 Solution
Question 5 :
If α and β are the roots of
2x2-3x-5 = 0
form a quadratic equation whose roots are α2 and β2
Question 6 :
If α and β are the roots of
x2-3x+2 = 0
form a quadratic equation whose roots are -α and -β.
Question 7 :
If α and β are the roots of
x2-3x-1 = 0
then form a quadratic equation whose roots are 1/α2 and 1/β2. Solution
Question 8 :
If α and β are the roots of the equation
3x2-6x+1 = 0
form an equation whose roots are
(i) 1/α , 1/β (ii) α2β , β2α (iii) 2α+β, 2β+α
Question 9 :
If one root of the equation
2x2-ax+64 = 0
is twice the other, then find the value of a.
Question 10 :
If α and β are the roots of
5x2-px+1 = 0
and α - β = 1, then find p. Solution
Question 11 :
If one root of the equation
3x2+kx-81 = 0
is the square of the other, find k. Solution
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