Home
Class 12
MATHS
What is the sum of all values of m that ...

What is the sum of all values of m that satisfy `2m^(2)-16m+8=0` ?

A

-8

B

`-4sqrt(3)`

C

`4sqrt(3)`

D

8

Text Solution

Verified by Experts

Choice D is correct. The problem asks for the sum of the roots of the quadratic equation `2m^(2)-16m+8=0`. Dividing each side of the equation by 2 gives `m^(2)-8m+4=0`. If the roots of `m^(2)-8m+4=0` are `s_(1) and s_(2)`, then the equation can be factored as `m^(2)-8m+4=(m-s_(1))(m-s_(2))=0`. Looking at the coefficient of x on each side of `m^(2)-8m+4=(m-s_(1))(m-s_(2))` gives `-8= -s_(1)-s_(2), or s_(1)+s_(2)=8`.
Alternatively, one can apply the quadratic formula to either `2m^(2)-16m+8=0` or `m^(2)-8m+4=0`. The quadratic formula gives two solutions, `4-2sqrt(3)` and `4+2sqrt(3)` whose sum is 8.
Choices A, B, and C are incorrect and may result from calculation errors when applying the quadratic formula or a sign error when determining the sum of the roots of a quadratic equation from its coefficients.
Promotional Banner

Similar Questions

Explore conceptually related problems

m^2-m+1=0 find the value of m

The number of integral values of m for which the equation (1+m^(2)) x^(2) - 2(1+3m)x+(1+8m) = 0 , has no real roots is

The real value of a for which the value of m satisfying the equation (a^2-1)m^2-(2a-3)m+a=0 given the slope of a line parallel to the y-axis is(a) 3/2 (b) 0 (c) 1 (d) +-1

For what value of m is x^(3)-2mx^(2)+16 Divisible by x+2 ?

The product of all the solutions to the equation 3y ^(2)+4v -2 =0 is M. What is the value of M ?

Find all values of 'm' which (2m-3)x^(2)+2mx+4 lt 0 for all real x.

Find the sum of the possible integer values of m: 2m+n=10 m(n-1)=9

The real value of a for which the valye of m satisfying the equation (a^(2)-1)m^(2)-(2a-3)m +a =0 gives the slope of a line parallel to the y-axis is

Let S be the sum of all possible determinants of order 2 having 0,1,2 and 3 as their elements,. Find the common root alpha of the equations x^(2)+ax+[m+1]=0, x^(2)+bx+[m+4]=0 and x^(2)-cx+[m+15]=0 such that alphagtS wherea+b+c=0 and m=sum_(n to 00)(1)/(n)sum_(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2))) and [.] denotes the greates integer function.

Four paticle of masses m_1 = 2 m, m_2 = 4 m, m_3 = m and m_4 are placed at four corners of a square. What should be the value of m_4 so that the centres of mass of all the four particle are exactly at the centre of the square ?