Question

If (x - a) is the factor of 3x2

- mx - na then prove that a =m+n/3​

Answer 1

Given:

• If (x - a) is the factor of 3x² - mx - na

To prove:

• a = (m + n)/3

Solution:

If (x - a) is the factor of 3x² - mx - na then substituting x = a will give the answer as zero.

=> 3a² - ma - na = 0

=> 3a² - a (m + n) = 0

Dividing equation throughout by a, we get

=> 3a - (m+n) = 0

=> 3a = (m + n)

=> a = (m + n)/3

Hence proved.

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Extra information:

For quadratic polynomial which has zeroes $\sf{\alpha}$ and $\sf{\beta}$

$\sf{\alpha+\beta=\dfrac{-b}{a}}$

$\sf{\alpha\beta=\dfrac{c}{a}}$

Answer 2

Given :-

• (x - a) is the factor of 3x² - mx - na

To Prove :-

• a = m+n/ 3

Solution :-

★ As ( x - a ) is the factor of 3x² - mx - na, then substituting x = a definitely give the answer 0.

➪ 3a² - ma - na = 0

➪ 3a² - a (m + n) = 0

➪ 3a - (m + n) = 0 [divide whole equation by a ]

➪ 3a = m + n

➪ a = (m + n)/ 3

Hence, ProVed.

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