`x^2+(a-b)x+(1-a-b)=0, a,b in R` find the condition on `a` for which both roots of the equation are real and unequal

If x^(2)+(a-b)x=(1-a-b)=0. where a,b in R then find the values of a for which equation has unequal real roots for all values of b .

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 b are real and aneb then show that the roots of the equation (a-b)x^(2)+5(a+b)x-2(a-b)=0 are real and unequal.

If a,b,c in R, then find the number of real roots of the equation x,c,-b-c,x,ab,-a,x]|=0

show that the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 where a,b,c in R are always real.Find the condition that the roots may be equal.what are the roots when this condition satisfied.

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

Find the condition if the equation 3x^(2)+4ax+b=0 has at least one root in (0,1).

If the roots of the equation x^(2)+2cx+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 a,b,c, in R, find the number of real root of the equation |{:(x,c,-b),(-c,x,a),(b,-a,x):}| =0