(a²+b²)x² – 2(ac+bd)x + c² + d² = 0 If the following equation has equal roots, then a) ab = cd b) ad = bc c) ad = √bc

Question

(a²+b²)x² – 2(ac+bd)x + c² + d² = 0
If the following equation has equal roots, then
a) ab = cd b) ad = bc c) ad = √bc d) ab = √cd

please answer

in progress 0
Anna 3 weeks 2021-08-21T23:08:32+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-21T23:10:09+00:00

    Answer:

    Option b) ad = bc

    Step-by-step explanation:

    For equal roots of Ax²+Bx+C=0, B²-4AC=0

    Here, A=(a²+b²), B= – 2(ac+bd), C=(c²+d²)

    ∴ B²-4AC=[ – 2(ac+bd)]² – 4(a²+b²)(c²+d²)

    Since B²-4AC=0, B² = 4AC

    ∴ [ – 2(ac+bd)]² = 4(a²+b²)(c²+d²)

    4[(a²c²+b²d²+2abcd)] = 4[a²(c²+d²)+b²(c²+d²)] = 4[a²c²+a²d²+b²c²+b²d²)]

    a²c²+b²d²+2abcd = a²c²+a²d²+b²c²+b²d²

    (cancelling similar terms on both sides)

    ∴ 2abcd = a²d²+b²c²

    or (ad)²+(bc)²=2abcd

    (ad)²+(bc)²-2abcd = 0

    ∴ (ad-bc)²=0

    or ad-bc=0

    ad = bc

    0
    2021-08-21T23:10:16+00:00

    Answer:

    (a^2 + b^2)x^2 – 2(ac + bd)x + (c^2 + d^2) = 0 has equal roots.Therefore, discriminant = 0 Thus [2(ac + bd)]^2 + 4(a^2 + b^2) (c^2 + d^2) a^2c^2 + …

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )