Question

7. If the equations x2 - ax + b = 0 and x2 – ex + f = 0 have one root in common and if the sea
equation has equal roots, then prove that ae = 2(b + f).​

Answer 1

Answer:

ae = 2(b + f)

Step-by-step explanation:

If the equations x2 - ax + b = 0 and x2 – ex + f = 0 have one root in common and if the second equation has equal roots, then prove that ae = 2(b + f).​

x² - ex + f = 0

roots are equal

if e² = 4f

roots are = e/2

x² -ax + b = 0

=> roots are

one of (a ± √a² - 4b)/2   = e/2

one of ±√a² - 4b = e - a

squaring both sides one of them

=> a² - 4b = e² + a² -2ae

=> 2ae = e² + 4b

using e² = 4f

=> 2ae = 4f + 4b

=> ae = 2f + 2b

=>  ae = 2b + 2f

=> ae = 2(b + f)

QED

Proved

Answer 2

Answer:

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