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Question

(i) Find the value of k for which x=1 is a root of the equation x2+kx+3=0. Also, find the other root. 
(ii) Find the values of a and b for which x=34 and x=-2 are the roots of the equations ax2+bx6=0


Solution

(i) x2+kx+3=0
one root is given x=1
(1)2+k(1)+3=0
1+k+3=0
k=4

Now using this our quadratic equation would be 
 
x24x+3=0
x2(3+1)x+3=0
x23xx+3=0
x(x3)1(x3)=0
(x3)(x1)=0
so our roots are
x=3 and 1

(ii) Given roots 
α=34  and  β=2
x2(α+β)x+αβ
x2(342)x+(34)×(2)=0
x2(54)x+(32)=0
x2+54x32=0
4x2+5x6=0
we have 
ax2+bx6=0

so a=4 and b=5


Mathematics
Secondary School Mathematics X
Standard X

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