Find the value of x, if `a+7=0`,
`b+10=0` and `12x^(2)=ax-b`.

Find the value of x, if a+1=0 and x^(2)+ax-6=0 .

Find the least value of f(x)=a x+b/x , where a >0,\ \ b >0 and x >0 .

Find the roots of x^2+7x+12=0

Find the value of a and b if x-1 and x-2 are factors of x^3-ax+b .

Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x for each real x. Statement-2: If a, b, c in R such that ax^(2) + bx + c = 0 for three distinct real values of x, then a = b = c = 0 i.e. ax^(2) + bx + c = 0 for all x in R .

Find the value of x, given that: A^2=B, A=[{:(,2,12),(,0,1):}] and B=[{:(,4,x),(,0,1):}]

Find the range of values of x for which the expression 12x^(2)+7x-10 is negative.

Find the values of a and b so that the polynomial x^3+10 x^2+ax+b is exactly divisible by x-1 as well as x-2.

If the equation x ^(2) +ax+12 =9, x ^(2) +bx +15 =0 and x^(2) + (a+b) x +36=0 have a common positive root, then b+2a equal to.

Find the value of 'a' and 'b' lim_(x to 2) and lim_(x to 4) exists where f(x){{:(x^(2)+ax+b,0lexlt2),(3x+2,2lexle4),(2ax+5b,4ltxle8):}