If `a and c` are the lengths of segments of any focal chord of the parabola `y^2=2b x ,(b >0),` then the roots of the equation `a x^2+b x+c=0` are (a) real and distinct (b) real and equal (c) imaginary (d) none of these

If b\ a n d\ c are lengths of the segments of any focal chord of the parabola y^2=4a x , then write the length of its latus rectum.

If a, a_1 ,a_2----a_(2n-1),b are in A.P and a,b_1,b_2-----b_(2n-1),b are in G.P and a,c_1,c_2----c_(2n-1),b are in H.P (which are non-zero and a,b are positive real numbers), then the roots of the equation a_nx^2-b_nx |c_n=0 are (a) real and unequal (b) real and equal (c) imaginary (d) none of these

If the roots of the equation x^2+2c x+a b=0 are real and unequal, then the roots of the equation x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational

The expression ax^2+2bx+b has same sign as that of b for every real x, then the roots of equation bx^2+(b-c)x+b-c-a=0 are (A) real and equal (B) real and unequal (C) imaginary (D) none of these

If a+b+c=0, a,b,c in Q then roots of the equation (b+c-a) x ^(2) + (c+a-c) =0 are: Rational Irrational Imaginary none of these .

If a,b, cinR , show that roots of the equation (a-b)x^(2)+(b+c-a)x-c=0 are real and unequal,

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If the roots of the equation , x^2+2c x+ab=0 are real and unequal, then the roots of the equation, x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: a. real and unequal b. real and equal c. imaginary d. Rational

If the roots of the equation ax^2 + bx + c = 0, a != 0 (a, b, c are real numbers), are imaginary and a + c < b, then

If a, b, c are real and a!=b , then the roots ofthe equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :