Question

If (x-3) is one factor of x square + ax - 4 =0 and x square - 4x + b = 0, then 2a - b is equal to

Answer 1

p(x)=x^2+ax-4
and f(x)=x^2-4x+b
Since x-3 is a factor of both
p(3)=0
And f(3)=0
Therefore 3^2+3a-4=0
=》9+3a-4=0
=>5+3a=0
=>3a=-5y
=>a= -5/3
Now f(3) =3^2-4×3+b=0y
=>9-12+b=0
=>b=3u
Therefore 2a-b=2(-5/3)-3
=>-10/3-3
=>-10-9/3
=>-19/3

Answer 2

Gɪᴠᴇɴ :-

If (x-3) is one factor of x square + ax - 4 =0 and x square - 4x + b = 0

ᴛᴏ ғɪɴᴅ :-

Value of (2a - b)

sᴏʟᴜᴛɪᴏɴ :-

➡ (x - 3) is a factor of both equation :-

➡ x² + ax - 4 = 0

➡ x² - 4x + b = 0

And,

➡ (x - 3) is a factor

So,

➡ x - 3 = 0

➡ x = 3

By usnig factor theorem, we get,

↣ f(x) = x² + ax - 4 = 0

↣f(3) = 3² + a×3 - 4 = 0

↣ 9 - 4 + 3a = 0

↣ 3a + 5 = 0

↣ a = -5/3

Now,

↣ f(x) = x² - 4x + b = 0

↣ f(3) = 3² - 4×3 + b = 0

↣ 9 - 12 + b = 0

↣ b - 3 = 0

↣ b = 3

Now,

➦ 2a - b = 2×-5/3 - 3

➦ -10/3 - 3

➦ (-10 - 9) / 3

➦ -19/3

Hence,

➲ (2a - b) = -19/3