If a and b are roots of quadratic polynomial 2x^2+5x+k ,find the value of k such that (a+b)^2-ab=24.
paras:
what is the meaning of this sign which is after 2x
this sign means 2x to the power 2
i.e. 2x sq.
ok
i think that your ques should be (a+b)^2-ab=21/4
how can you say so,Ichha? please give me the logic behind this.
Answers
Answered by
15
roots are a and b
p(x)=2x²+5x+k
α+β= - b/a
so, a+b= - b/a
= - 5/2
αβ=c/c
so, ab=c/a = k/2
given that, (a+b)²-ab=24
so, ( - 5/2)²-k/2 = 24
25/4 -k/2 = 24
25-2k/4=24
25-2k=24×4
-2k=96-25
k=71/-2
k= -35.5
p(x)=2x²+5x+k
α+β= - b/a
so, a+b= - b/a
= - 5/2
αβ=c/c
so, ab=c/a = k/2
given that, (a+b)²-ab=24
so, ( - 5/2)²-k/2 = 24
25/4 -k/2 = 24
25-2k/4=24
25-2k=24×4
-2k=96-25
k=71/-2
k= -35.5
Answered by
10
p(x) = 2x^2 + 5x + k
compair with Ax^2 + Bx + C
A = 2, B = 5, C = k
if roots of the equation is a and b then ,
a + b = -B/A = -5/2
ab = C/A = k/2
given (a + b)^2 - ab = 24
putting the value of a +b and ab
(-5/2)^2 - k/2 = 24
25/4 - k/2 = 24
-71/4 = k/2
k = -71/2
compair with Ax^2 + Bx + C
A = 2, B = 5, C = k
if roots of the equation is a and b then ,
a + b = -B/A = -5/2
ab = C/A = k/2
given (a + b)^2 - ab = 24
putting the value of a +b and ab
(-5/2)^2 - k/2 = 24
25/4 - k/2 = 24
-71/4 = k/2
k = -71/2
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