6 If Roots Of Equation A2 B2 X2 2 Ac Bd X C2 D2 0 Has Equal Roots Pr If the roots of the equation (a 2 b 2) x 2 2 (a c b d) x (c 2 d 2) = 0 are equal, prove that a b = c d. it is given that the roots of the equation ` (a^2 b^2)x^2 2 (ac bd)x (c^2 d^2)=0 are equal. ∴ d = 0. ⇒ [ 2 (a c b d)] 2 4 (a 2 b 2) (c 2 d 2) = 0. If the roots of the equation (a2 b2)x2 − 2(ac bd)x (c2 d2) = 0 are equal, prove that ba = dc. roots are real only when the discriminant d is positive or 0. since d = 4 (ad bc)^2, then roots are real only when ad bc = 0, ie, ad = bc. now, using the quadratic formula we get just one root = (ac bd) (a^2 b^2).
7 If The Roots Of The Equation X2 2cx Ab 0 Are Real Unequal Prove That The nature of the roots of a quadratic equation depends on the discriminant. the discriminant is \[d = {b^2} 4ac\]. if, \[d > 0\], then the roots of the quadratic equation are real and different. if, \[d < 0\], then the roots of the quadratic equation are imaginary. if, \[d = 0\], then the roots of the quadratic equation are real and equal. In the following, determine whether the given quadratic equation have real roots and if so, find the roots: `2x^2 5sqrt3x 6=0` which of the following are the roots of `3x^2 2x 1=0`. If equation has (a2 b2)x2−2(ac bd)x (c2 d2)=0 equal roots , then prove that a b= c d. q. (i) if the roots of the equation a 2 b 2 x 2 2 a c b d x c 2 d 2 = 0 are equal, prove that a b = c d. [cbse 2017] (ii) if ad ≠ bc then prove that the equation a 2 b 2 x 2 2 a c b d x c 2 d 2 = 0 has no real roots. [cbse 2017] q. If the roots of the equations ax 2 2bx c = 0 and b x 2 − 2 ( a c) x b = 0 are simultaneously real, then prove that b 2 = ac. view all practice questions from mathematics class 10 (rd sharma).
7 If The Roots Of The Equation A B X2 B C X C A 0 Are Equal Prove T If equation has (a2 b2)x2−2(ac bd)x (c2 d2)=0 equal roots , then prove that a b= c d. q. (i) if the roots of the equation a 2 b 2 x 2 2 a c b d x c 2 d 2 = 0 are equal, prove that a b = c d. [cbse 2017] (ii) if ad ≠ bc then prove that the equation a 2 b 2 x 2 2 a c b d x c 2 d 2 = 0 has no real roots. [cbse 2017] q. If the roots of the equations ax 2 2bx c = 0 and b x 2 − 2 ( a c) x b = 0 are simultaneously real, then prove that b 2 = ac. view all practice questions from mathematics class 10 (rd sharma). If the roots of the equation (a 2 b 2)x 2 − 2 (ac bd)x (c 2 d 2) = 0 are equal, prove that a b = c d. solution show solution the given quadric equation is (a 2 b 2 )x 2 − 2 (ac bd)x (c 2 d 2 ) = 0, and roots are real. Show that if the roots of the following quadratic equation in x (a² b²)x² 2 (ac bd)x (c² d²)=0 are equal then ad=bc. doubt by zoha. solution : (a² b²)x² 2 (ac bd)x c² d²=0. b= 2 (ac bd) c=c² d². hence proved. if root of the equations (a² b²)x 2 (ac bd)x c² d²=0 are equal then prove that a b=c d. It is given that the roots of the equation (a2 b2)x2 2 (ac bd)x (c2 d2) = 0 are equal. ∴ d = 0. hence proved. 34. if the roots of the equation (a2 b2) x2 2(ac bd) x (c2 d2) = 0 are equal, prove that a b=c d.
6 Prove That If The Roots Of The Quadratic Equation C2 Ab X2 2 A2 Bc X If the roots of the equation (a 2 b 2)x 2 − 2 (ac bd)x (c 2 d 2) = 0 are equal, prove that a b = c d. solution show solution the given quadric equation is (a 2 b 2 )x 2 − 2 (ac bd)x (c 2 d 2 ) = 0, and roots are real. Show that if the roots of the following quadratic equation in x (a² b²)x² 2 (ac bd)x (c² d²)=0 are equal then ad=bc. doubt by zoha. solution : (a² b²)x² 2 (ac bd)x c² d²=0. b= 2 (ac bd) c=c² d². hence proved. if root of the equations (a² b²)x 2 (ac bd)x c² d²=0 are equal then prove that a b=c d. It is given that the roots of the equation (a2 b2)x2 2 (ac bd)x (c2 d2) = 0 are equal. ∴ d = 0. hence proved. 34. if the roots of the equation (a2 b2) x2 2(ac bd) x (c2 d2) = 0 are equal, prove that a b=c d.