Show that the equation `2(a^2+b^2)x^2+2(a+b)x+1=0` has no real roots when `a!=b`

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

If the roots of the equation x^(2)+2cx+ab=0 are real unequal,prove that the equation x^(2)-2(a+b)x+a^(2)+b^(2)+2c^(2)=0 has no real roots.

Prove that the quadratic equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 will have no real root if aneb .

Prove that the equation x^(2)(a^(2)b^(2))+2x(ac+bd)+(c^(2)+d^(2))=0 has no real root if adnebc .

If a, b, c in R and the quadratic equation x^2 + (a + b) x + c = 0 has no real roots then

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a) 6 real roots b) at least 2 real roots c) 4 real roots d) none of these

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

If a,b,c in R and the quadratic equation x^(2)+(a+b)x+c=0 has no real roots then

Suppose a,b in R. If the equation x^(2)-(2a+b)x+(2a^(2)+b^(2)-b+1//2)=0 has two real roots, then