Show that the roots of `(b+c)x^2-(a+b+c)x+a=0`are rational .where a,b,c are rational.

Show that the roots of each of the following equations are rational(a,b,c are rational): (b+c)x^2-(a+b+c)x+a=0

Show that the roots of each of the following equations are rational(a,b,c are rational): (a-b+c)x^2+2cx+(b+c-a)=0

Show that the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal if a,b,c are in H.P.

Two roots of x^2 - (a + b)x + ab = 0 (a, b are rational) are____

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

If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the roots of (b+c-a)x^2+(c+a-b)x+(a+b-c)=0 are real and distinct.

If tanA, tanB are the roots of the quadratic abx^2-c^2x+ab=0, where a,b,c are the sides of a triangle. then

IF a,b,c are rational and a+b+c=0, show that the roots of the equation ax^2+bx+c=0 are rational.

Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 are equal if either b=0 or , a^3+b^3+c^3-3abc=0

If (log)_a x=b for permissible values of a and x , then identify the statement(s) which can be correct. (a)If a and b are two irrational numbers, then x can be rational. (b)If a is rational and b is irrational, then x can be rational. (c)If a is irrational and b is rational, then x can be rational. (d)if aa n d b are rational, then x can be rational.