If x-a is a factor of x2-p x-q and x2-m x-n then the value of a in terms of n- q- m and p is-

( a)² + p·( a) + q = 0 – gt; a² ap + q = 0 ( a)² + m·( a) + n = 0 – gt; a² am + n = 0 Since they both equal 0, you can set them equal to each other: a² ...

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Standard IX

Mathematics

Factor Theorem

If x+a is a f...

Question

If x + a is a factor of x² + px + q and x² + mx + n then the value of a in terms of n, q, m and p is?

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Solution

(-a)² + p·(-a) + q = 0 --> a² -ap + q = 0
(-a)² + m·(-a) + n = 0 --> a² -am + n = 0
Since they both equal 0, you can set them equal to each other:
a² -ap + q = a² -am + n
-ap + q + -am + n
am - ap = n-q
a(m-p) = n-q

a=n-q/m-p

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If x + a is a factor of x2 + px + q and x2 + mx + n then the value of a in terms of n, q, m and p is?

(-a)² + p·(-a) + q = 0 --> a² -ap + q = 0 (-a)² + m·(-a) + n = 0 --> a² -am + n = 0 Since they both equal 0, you can set them equal to each other: a² -ap + q = a² -am + n -ap + q + -am + n am - ap = n-q a(m-p) = n-q a=n-q/m-p

If x + a is a factor of x² + px + q and x² + mx + n then the value of a in terms of n, q, m and p is?

(-a)² + p·(-a) + q = 0 --> a² -ap + q = 0
(-a)² + m·(-a) + n = 0 --> a² -am + n = 0
Since they both equal 0, you can set them equal to each other:
a² -ap + q = a² -am + n
-ap + q + -am + n
am - ap = n-q
a(m-p) = n-q

a=n-q/m-p