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answers:
Deepak Suwalka say: x = 3 ⇒ (x - 3) = 0
x = 8 ⇒ (x - 8) =0
Therefore factors will be
(x - 3)(x - 8) = 0
Now, extand the factors
x² - 8x - 3x + 24 = 0
Therefore,
x² - 11x + 24 = 0
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himanshu say: Put (x-3)*(x-8) =0
x^2-3x-8x+24=0
X^2-11x+24=0
Is the required equation
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Jill say: the quadratic function, whose roots are a and b, is f(x) = k[x² - (a + b)x + ab], where k is a real number
therefore, the quadratic function, whose roots are 3 and 8, is f(x) = k[x² - (3+ 8)x + 3*8]
f(x) = k(x² - 11x + 24)
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ImpelTutors say: The quadratic function, whose roots are a and b, is f(x) = K[x² - (a + b)x + ab], where K is a real number
Therefore, The quadratic function, whose roots are 3 and 8, is f(x) = K[x² - (3+ 8)x + 3*8]
f(x) = K(x² - 11x + 24)
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Mathmom say:
They are asking for function, not equation.
So we need y or f(x), not just x's.
Since x = 3 is a root, then x−3 is a factor
Since x = 8 is a root, then x−8 is a factor
y = a (x − 3) (x − 8)
y = a (x² − 11x + 24)
This is the general function for a quadratic with roots 3 and 8.
For a particular function, just choose any value you want for a.
You can make it simple, and use a = 1
y = x² − 11x + 24
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Huh!? say: Solutions: x = 3; x = 8
Set equal to zeros: x - 3 = 0 ; x - 8 = 0.
Multiply the expressions together.
y = (x - 3)(x -8),
and make it a function, so we need a y.
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Krishnamurthy say: f(x) = x^2 - 11x + 24
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The Death Bunny say: where either x-8 = 0
or x -3 = 0
0 = (x-3) (x-8)
0 = x^2 - 3x - 8x + 24
0 = x^2 - 11x + 24
or
-24 = x^2 -11x
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Mr say: Since the roots are x = 3 and x = 8, the quadratic is in the form (x - 3)(x - 8) = 0, so we now just need to expand this:
(x - 3)(x - 8) = x² - 3x - 8x + 24 = x² - 11x + 24
So f(x) = x² - 11x + 24
Note that there are infinitely many solutions to the question, multiplying f(x) by a constant value would still have roots:
x = 3 and x = 8.
In general f(x) = C ( x² - 11x + 24 ), where C is constant.
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ProfRay say: (x - 3)(x - 8) = 0
Now expand to get standard format
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Julia say: (x - 3) (x - 8) = 0
x2 - 8x - 3x + 24 = 0
x2 - 11x + 24 = 0
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roger say: (x-3)(x-8)=0
x^2-11x+24=0
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