x^(2)-7x+12=0

Discuss the nature of the following quadratic equations without finding the roots i) x^(2)-12x+32=0 ii) 2x^(2)-7x+10=0 iii) 4x^(2)-20x+25=0 iv) 3x^(2)+7x+2=0

Discuss the nature of the following quadratic equations without finding the roots i) x^(2)-12x+32=0 ii) 2x^(2)-7x+10=0 iii) 4x^(2)-20x+25=0 iv) 3x^(2)+7x+2=0

The number of real roots of |x|^(2)-7|x|+12=0 is :

If two roots of x^(3)7x^(2)+4x+12=0 are in the ratio 1:3 then the roots are

Let S is the region of points which satisfies y^(2)lt16x,x lt4 and (xy(x^(2)-3x+2))/(x^(2)-7x+12)gt0 . Its area is

Let S is the region of points which satisfies y^(2)lt16x,x lt4 and (xy(x^(2)-3x+2))/(x^(2)-7x+12)gt0 . Its area is

Assertion (A ) : the number of roots of x^4 +2x^3 -7x^2 -8x +12=0 Reason (R ) : Every algebraic equation of degree n has n roots and nomore .

Assertion (A ) : the number of roots of x^4 +2x^3 -7x^2 -8x +12=0 Reason (R ) : Every algebraic equation of degree n has n roots and nomore .

The equation to the pair of lines passing through (1,-1) and parallel to the pair of lines x^(2)-7 x y+12 y^(2)=0 is