Home
Class 12
MATHS
Find A+B if A = [(2,5),(3,6)] and B = ...

Find `A+B if A = [(2,5),(3,6)] and B = [ (7,9),(6,5)]`

Text Solution

Verified by Experts

The correct Answer is:
`(A) rarr (p,r); (B) rarr (s); (C) rarr (q); (D) rarr (s)`
`(A) rarr (p,r), (B) rarr (s), (C) rarr (q), (D) rarr (s)`
On comparing, we get
`{4f(-1)-3}a^(2) + {4f(1)-3} a+f(2)=0`
`{4f(-1)-3}b^(2) + {4f(1)-3} b+f(2)=0`
and `{4f(-1)-3}c^(2) + {4f(1)-3}C+f(2)=0`
It is clear that a, b, c are the roots of
`{4f(-1)-3}x^(2) + {4f(1)-3}x+f(2)=0` then
`4f(-1)-3=0, 4f(1)-3=0,f(2)=0`
`rArr f(-1)=3/4,f(1)=3/4,f(2)=0` Let `f(x) = (x-2) (ax+b)`
Now, `f(-1) = 3/4 rArr (-3) (-a+b) =3/4 rArr a-b = 1/4 `
`f(1) = 3/4 rArr (-1) (-a+b) =3/4 rArr a+b = -3/4 `
`therefore a= -1/4 , b = -1/2`
`rArr f(x) = 1/4 (4-x^(2))`
Graph of `y = f(x)`

(A) x- coordinates of the point intersection of `y = f(x) ` with
ther X- axis are - 2 and 2.
(B) Area `=3/2 int_(-2)^(2) 1/4 (4-x^(2)) dx = 3/4 int _(0)^(2) (4-x^(2)) dx`
`= 3/4 [4x-x^(3)/3]_(0)^(2)= 3/4xx 16/3 = 4`
(C) Maximum value of `f(x)` is 1.
(D) Length of intercept on the X_ axis is 4.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find AB, if A=[(6,9),(2,3)] and B=[(2,6,0),(7,9,8)] .

Find |A| If A = [(7x , 3), (5 , 6)]

Solve the following equations by matrix method. Let A = [(3,7),(2,5)] and B = [(6,8),(7,9)] verify that (AB)^(-1) = B^(-1)A^(-1) .

If 2A+3B = [(2,-1,4),(3,2,5)] and A+2B=[(5,0,3),(1,6,2)] , then B =

Find B-A if A={2,3,4} and B={3,4,5,6}

Let A= {:[( 3,7),( 2,5) ]:} and B = {:[( 6,8),( 7,9) ]:} .Verify that (AB) ^(-1) =B^(-1) A^(-1)

Find the matrix X so that X[(1,2,3),(4,5,6)]=[(-7,-8,-9),(2,4,6)]

Find A cap B when A={5,6,7,8} and B={7,8,9,10}

If A = [{:( 1 , 2 ) , (5 , 6) :}] , B = [{:( 3 , 5 ) , (x , -4) :}] and A + B = [{:( 4 , 7 ) , (6 , 2) :}] , then the value of x must be