If `f(x)=|x+a^2 a b ac a b x+b^2 bc a c b c x+c^2|, t h e n` prove that `f^(prime)(x)=3x^2+2x(a^2+b^2+c^2)dot`

Similar Questions

Explore conceptually related problems

"If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," then prove that " f'(x)=3x^(2)+2x(a^(2)+b^(2)+c^(2)) .

If tanthetaa n dsectheta are the roots of a x^2+b x+c=0, then prove that a^4=b^2(b^2-4ac)dot

If ( x + a) ( x + b ) (x + c ) = x^(3) + 14x^(2) + 59x + 70 , find the value of a^(2) + b^(2) + c^(2)

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

If s intheta,costheta be the roots of a x^2+b x+c=0 , then prove that b^2=a^2+2ac.

If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig A) a c 0 c) a b >0 d ) a b c<0

If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a. a^2+c^2=-a b b. a^2-c^2=-a b c. a^2-c^2=a b d. none of these

If ( x + a) ( x + b ) (x + c ) = x^(3) + 14x^(2) + 59x + 70 , find the value of (a)/( bc) + ( b)/( ac) + ( c )/( ab)

If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,w h e r ea c!=0, then prove that f(x)g(x)=0 has at least two real roots.

Prove that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0