the answer therefore is 40

a is 3 root 5 b 8s -3root 5

photo is not clear and it is of icic.board

it will be -3 not sure

Hence, we gota= -49/41b= -21/41

We need to find the values ofaaandbb, such that the polynomialx3−10x2+ax+bx^3-10x^2+ax+bis exactly divisible byx−1x-1as well asx−2x-2

Assume that :f(x)=x3−10x2+ax+bfx=x3-10x2+ax+b

Using remainder theorem, we know that if a polynomialf(x)f(x)is divided byx−cx-c, the remainder isf(c)f(c)x−1=0⇒x=1x-1=0⇒x=1

Applying the factor theorem, we know that:

f(x)will be exactly divisible by(x−1)iff(1)=0fxwill be exactly divisible byx-1iff1=0.

Hence, we have:

f(1)=13−10×12+a×1+b=(1−10+a+b)=−9+a+bf1=13-10×12+a×1+b=1-10+a+b=-9+a+b∴f(1)=0⇒a+b=9...(1)f1=0⇒a+b=9...1

The same method must be applied for the second factor as well,x−2=0⇒x=2x-2=0⇒x=2

Similarly, applying the factor theorem gives us:

f(x)will be exactly divisible by(x−2)iff(2)=0fxwill be exactly divisible byx-2iff2=0.

Hence, we have:

f(2)=23−10×22+a×2+b=(8−40+2a+b)=−32+2a+bf2=23-10×22+a×2+b=8-40+2a+b=-32+2a+b∴f(2)=0⇒2a+b=32...(2)f2=0⇒2a+b=32...2

Solving simultaneously, by subtracting (1)from (2),we have:a=23Solving simultaneously, by subtracting (1)from (2),we have:a=23

Substituting the value ofainto11or22, we get the value ofbwhich is−-14.∴a= 23 andb=−-14

hence,wegot-49/41a -21/41

a= -49/41b= -12/41it is the right answerhope it helps u

a=-49/41

b= -21/41 this is the answer

a is 3 root 5b 8s-3root 5

a is 3 root 5b 8s -3root 5

first of all 2 + 3√5------------ = a + b√52 - 3√5

then2 + 3√5 2 + 3√5------------ x ---------- = a + b√52 - 3√5 2 + 3√5

4+ 45 +12√5------------------- = a + b√5 4 - 45

49 12√5---- - ----- = a + b√5-41 41

now comparison the both sides

a = -49/41b = -12/41

A is 3 root 5 B is 8 -3 root 5 this is very right answer

a= -49/45. and b=-12/41 this is write answer

value of a is 49and value of b is 12

a=(-49/41)B=(-21/41)