6 Prove That If The Roots Of The Quadratic Equation C2 Ab X2 2 A2 Bc X

Q Cdot If Roots Of The Quadratic Equation X 2 2 P X M N 0 If the roots of the equation (c 2 – ab) x 2 – 2 (a 2 – bc) x b 2 – ac = 0 in x are equal, then show that either a = 0 or a 3 b 3 c 3 = 3abc. the given quadric equation is (c 2 a b) x 2 2 (a 2 b c) x (b 2 a c) = 0. then prove that either a = 0 or a 3 b 3 c 3 = 3 a b c. here. If the roots of the equation (c2 −ab)x2 −2(a2 −bc)x (b2 −ac) = 0 are real ane equal, show that either a = 0 or (a3 b3 c3)= 3abc.

Solved I Algebra Solve Quadratic Equations The Two Roots Chegg The discriminant (d) of a quadratic equation ax^2 bx c = 0 is given by d = b^2 4ac. for the roots to be equal, d must be zero. hence, for our equation, the condition becomes ( 2(a^2 bc))^2 4(c^2 ab)(b^2 ac) = 0, which simplifies to 4(a^4 b^2c^2 2a^2bc) 4(b^2c^2 a^2c^2 a^3c abc^2). To prove that either a = 0 or a 3 b 3 c 3 = 3 ab c when the roots of the equation (c 2 − ab) x 2 − 2 (a 2 − b c) x b 2 − a c = 0 are equal, we will analyze the discriminant of the quadratic equation. for a quadratic equation of the form a x 2 b x c = 0, the discriminant is given by d = b 2 − 4 a c. if the roots of the. 6. prove that if the roots of the quadratic equation (c 2 − ab) x 2 − 2 (a 2 − b c) x (b 2 − a c) = 0 are equal, then a = 0 or a 3 b 3 c 3 = 3 ab c. [hint: here, d = {[2 (a 2 − b c)] 2 − 4 (c 2 − ab) (b 2 − a c)} = 0 ⇒ a (a 3 b 3 c 3 − 3 ab c) = 0.] 7. determine the positive value of k for which both the equations. If the roots of the equation (c 2 – ab)x 2 – 2 (a 2 – bc)x b 2 – ac = 0 are real and equal prove that either a = 0 (or) a 3 b 3 c 3 = 3abc. (c 2 – ab)x 2 – 2 (a 2 – bc)x b 2 – ac = 0. here a = c 2 – ab; b = – 2 (a 2 – bc); c = b 2 – ac. since the roots are real and equal. ∆ = b 2 – 4ac. [– 2 (a 2 – bc)] 2 – 4 (c 2 – ab) (b 2 – ac) = 0.

Find The Roots Fo The Quadratic Equation 6x 2 X 2 0 6. prove that if the roots of the quadratic equation (c 2 − ab) x 2 − 2 (a 2 − b c) x (b 2 − a c) = 0 are equal, then a = 0 or a 3 b 3 c 3 = 3 ab c. [hint: here, d = {[2 (a 2 − b c)] 2 − 4 (c 2 − ab) (b 2 − a c)} = 0 ⇒ a (a 3 b 3 c 3 − 3 ab c) = 0.] 7. determine the positive value of k for which both the equations. If the roots of the equation (c 2 – ab)x 2 – 2 (a 2 – bc)x b 2 – ac = 0 are real and equal prove that either a = 0 (or) a 3 b 3 c 3 = 3abc. (c 2 – ab)x 2 – 2 (a 2 – bc)x b 2 – ac = 0. here a = c 2 – ab; b = – 2 (a 2 – bc); c = b 2 – ac. since the roots are real and equal. ∆ = b 2 – 4ac. [– 2 (a 2 – bc)] 2 – 4 (c 2 – ab) (b 2 – ac) = 0. •equation is (c² ab)x² 2(a² bc)x (b² ac)=0. to prove: •a= 0 or •a³ b³ c³= 3abc. proof: we have, ⚫a= (c² ab) ⚫b= 2(a² bc) ⚫c= (b² ac) it is given that the equation has real & equal roots. therefore, d=0. we know the formula of the quadratic equation: =) b² 4ac=0. putting the value of a, b,& c in above equation. If the roots of the equation (c2 ab) x2 2 (a2 bc) x b2 ac = 0 are equal, prove that either a = 0 or a3 b3 c3 = 3abc. Let us consider a quadratic polynomial we know that if discriminant , the roots of the equation are equal. here ; ; therefore, discriminant=0 hence, proved. If the roots of the equation (c^2 ab)x^2 2 (a^2 bc) x b^2 ac=0 are equal, prove that either a=0 or a^3 b^3 c^3=3abc .more.

Solved What Is The Condition For A And C Such That The Roots Chegg •equation is (c² ab)x² 2(a² bc)x (b² ac)=0. to prove: •a= 0 or •a³ b³ c³= 3abc. proof: we have, ⚫a= (c² ab) ⚫b= 2(a² bc) ⚫c= (b² ac) it is given that the equation has real & equal roots. therefore, d=0. we know the formula of the quadratic equation: =) b² 4ac=0. putting the value of a, b,& c in above equation. If the roots of the equation (c2 ab) x2 2 (a2 bc) x b2 ac = 0 are equal, prove that either a = 0 or a3 b3 c3 = 3abc. Let us consider a quadratic polynomial we know that if discriminant , the roots of the equation are equal. here ; ; therefore, discriminant=0 hence, proved. If the roots of the equation (c^2 ab)x^2 2 (a^2 bc) x b^2 ac=0 are equal, prove that either a=0 or a^3 b^3 c^3=3abc .more.

What Are The Roots Of The Quadratic Equation Shown Chegg Let us consider a quadratic polynomial we know that if discriminant , the roots of the equation are equal. here ; ; therefore, discriminant=0 hence, proved. If the roots of the equation (c^2 ab)x^2 2 (a^2 bc) x b^2 ac=0 are equal, prove that either a=0 or a^3 b^3 c^3=3abc .more.