if the roots of the equation (b-c)x*2+(c-a)x+(a-b)=0are equal then.Prove that 2b=a+c
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if the roots of the equation (b-c)x*2+(c-a)x+(a-b)=0are equal then.Prove that 2b=a+c
your answer is here...
(b-c)x²+(c-a)x+(a-b)=0
Comparing with quadratic equation
Ax²+Bx+C=0
A=(b-c),
B=c-a,
C=a-b
Discriminate when roots are equal
D=B²-4AC=0
D=(c-a)²−4(b-c)(a-b)=0
D=(c²+a²−2ac)-4(ba-ac-b²+bc)=0
D=c²+a²−2ac-4ab+4ac+4b²-4bc=0
c²+a²+2ac-4b(a+c)+4b²=0
(a+c)²-4b(a+c)+4b²=0
[(a+c)-2b]²=0
a+c=2b
your answer is here...
(b-c)x²+(c-a)x+(a-b)=0
Comparing with quadratic equation
Ax²+Bx+C=0
A=(b-c),
B=c-a,
C=a-b
Discriminate when roots are equal
D=B²-4AC=0
D=(c-a)²−4(b-c)(a-b)=0
D=(c²+a²−2ac)-4(ba-ac-b²+bc)=0
D=c²+a²−2ac-4ab+4ac+4b²-4bc=0
c²+a²+2ac-4b(a+c)+4b²=0
(a+c)²-4b(a+c)+4b²=0
[(a+c)-2b]²=0
a+c=2b
Answered by
20
It has been prove that 2b=a+c if roots of the equation (b-c)x²+(c-a)x+(a-b)=0 are equal.
Given:
- A quadratic equation
To find:
- Prove that prove that 2b=a+c, if roots of the equation are equal.
Solution:
Concept to be used:
If roots of quadratic equation are equal than its discriminate is zero.
Step 1:
Write coefficients of x², x and constant term.
Step 2:
Put D=0
or
or
it is resembles to the identity
so,
thus,
taking square root both sides.
or
or
Thus,
It has been proven that 2b=a+c.
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