If α, β are the roots of ax 2 + bx + c = 0, (a ≠ 0

Question

If α, β are the roots of ax2 + bx + c = 0, (a ≠ 0) and a + δ, β + δ are the roots of Ax2 + Bx + c = 0, (A ≠ 0) for some constant δ, then prove that b2 – 4ac/a2 = B2 – 4AC/A2.

Navjyot Kalra · Accepted Answer

Sol. We know that,(α &ndash; &beta;)2 = [(α + &delta;) &ndash; (&beta; + &delta;)]2&rArr; (α + &beta;)2 - 4α &beta; = (α + &delta; + &beta; + &delta;)2 - 4(α + &delta;) (&beta; + &delta;)&rArr; b2/a2 &ndash; 4c/a = B2/A2 &ndash; 4C/A &rArr; 4ac &ndash; b2/a2 = 4AC &ndash; B2/A2[Hence α +&beta; = -b/a, α &beta; = c/a(α + &delta;) (&beta; + &delta;) = - B/A and (α + &delta;) (&beta; + &delta;) = C/A]Hence proved.

Algebra> If α, β are the roots of ax 2 + bx + c = ...

If α, β are the roots of ax2 + bx + c = 0, (a ≠ 0) and a + δ, β + δ are the roots of Ax2 + Bx + c = 0, (A ≠ 0) for some constant δ, then prove that b2 – 4ac/a2 = B2 – 4AC/A2.

Amit Saxena , 10 Years ago

Navjyot Kalra

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Ask a Doubt

What is a binomial expression?

Algebra

Can we divide two vectors? If this is possible then how?

Algebra

How do you write “the product of 18 and q” as an algebraic expression?

Algebra

दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे

Algebra

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?

Algebra

Algebra> If α, β are the roots of ax 2 + bx + c = ...

If α, β are the roots of ax2 + bx + c = 0, (a ≠ 0) and a + δ, β + δ are the roots of Ax2 + Bx + c = 0, (A ≠ 0) for some constant δ, then prove that b2 – 4ac/a2 = B2 – 4AC/A2.

Amit Saxena , 10 Years ago

Navjyot Kalra

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Ask a Doubt

Other Related Questions on Algebra

What is a binomial expression?

Algebra

Can we divide two vectors? If this is possible then how?

Algebra

How do you write “the product of 18 and q” as an algebraic expression?

Algebra

दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे

Algebra

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?

Algebra