SOLUTION: 5.If a+b+c=0,then 3a*x*x+2b*x+c=0 has
A.atleast one root in [-1,0]
B.atleast one root in [0,1]
C.atleast one root in [-1,1]
D.atleast one root in [0,2]
Algebra.Com
Question 31503: 5.If a+b+c=0,then 3a*x*x+2b*x+c=0 has
A.atleast one root in [-1,0]
B.atleast one root in [0,1]
C.atleast one root in [-1,1]
D.atleast one root in [0,2]
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
I DONT KNOW YOUR COURSE OF STUDY AND BACK GROUND KNOWLEDGE.I HOPE YOU KNOW CALCULUS AND ROLLE'S THEOREM.I AM ANSWERING ON THAT BASIS
CONSIDER F(X)=AX^3+BX^2+CX.....
WE HAVE
F(0)=A*0^3+B*0^2+C*0=0
F(1)=A*1^3+B*1^2+C*1=A+B+C=0..AS GIVEN....SO AS PER ROLLE'S THEOREM
WHEN A CONTINUOUSLY VARYING FUNCTION HAS 2 ZEROES AT BOTH ENDS OF AN INTERVAL...THEN ITS DERIVATIVE WILL HAVE A ZERO AT ONE POINT WITHIN THE INTERVAL.HENCE
DF/DX=3A*X^2+2B*X+C=0 BETWEEN X=0 AND X=1
SO B IS THE ANSWER
RELATED QUESTIONS
Which of the below option's are right?
If a+b+c=0,then 3a*x*x+2b*x+c=0 has
A.atleast... (answered by venugopalramana)
If a,b,c i.e the coefficients of the quadratic equation ax^2+bx+c=0 are in A.P and the... (answered by ikleyn)
Let f(0) = 0,f(pi/2)=1,f(3pi/2)=-1 be a continous and twice differentiable function.... (answered by vleith)
For what value of c will 3 x^2 - 2x + c = 0 have exactly one distinct real root?
A... (answered by mananth)
if f(x)=1-x which value is equivalent to f(i)
a. 0
b. 1
c. Square root of 2
d.... (answered by Fombitz)
Which one of the following is true:
a) 1/2 < 1/3 b) 12/25 < 11/21 c) 7/12 > (answered by rfer)
Find the value of k in x^2+3x+k-1=0 if the quadratic equation has:
a) equal roots
b)... (answered by Fombitz)
Which number is a root of f(x)=x^3+6x^2+9x that has multiplicity 1?
a. 3
b. 1
c.... (answered by jim_thompson5910)
One root of the polynomial equation 0=x^3-4x^2+9x-10 is 1-2i. Find an additional root.
(answered by robertb)