If `x^(2)+ax+10=0" and "x^(2)+bx-10=0` have a common root, then `a^(2)-b^(2)` is equal to

If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

For a ne b , if the equation x^(2)+ax+b=0" and "x^(2)+bx+a=0 have a common root, then the value of a+b=

If the equation x^(2)+2x+3=0 and ax^(2)+bx+c=0, a,b,c in R have a common root, then a:b:c is

If the quadratic equations 3 x^(2)+a x+1=0 and 2 x^(2)+b x+1=0 have a common root, then the value of the expression 5 a b-2 a^(2)-3 b^(2) is

If the equation x^(3)+k x^(2)+3=0 and x^(2)+k x+3=0 have a common root, then the value k .

If a x^(2)+b x+c=0 and b x^(2)+c x+a=0, a, b, c ne 0 have a common root, then value of ((a^(3)+b^(3)+c^(3))/(a b c))^(2) is

If the equation x^2 + px + q =0 and x^2 + p' x + q' =0 have common roots, show that it must be equal to (pq' - p'q)/(q-q') or (q-q')/(p'-p) .

If the equation x^2+b x-a=0"and" x^2-a x+b=0 have a common root, then a. a+b=0 b. a=b c. a-b=1 d. a+b=1

The equations x^(2) - 4x +a=0 and x^(2) + bx +5=0 have one root in common The other root of these equations are integers in the ratio 3 : 5Find the common root