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

The expression ax^2+2bx+c , where 'a' is non-zero real number, has same sign as that of 'a' for every real value of x,then roots of quadratic equation ax^2+ (b-c) x-2b-c -a-0 are: (a) real and equal (b) real and unequal (c) non-real having positive real part(d) non-real having negative real part

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

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 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

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 ax^3+bx^2+cx+d has local extremum at two points of opposite signs then roots of equation ax^2+bx+c=0 are necessarily (A) rational (B) real and unequal (C) real and equal (D) imaginary

Let a,b,c be real numbers in G.P. such that a and c are positive , then the roots of the equation ax^(2) +bx+c=0

The equation a x^2+b x+c=0 has real and positive roots. Prove that the roots of the equation a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0 re real and positive.

LET the equation ax^2+bx+c=0 has no real roots Assertion (A): c(a+b+c)gt0 , Reason (R): A quadratic expression ax^2+bx+c has signs same as that of al for all real x if the roots of the corresponding equation ax^2+bx+c=0 are imaginary. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.