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प्रश्न
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If one of the roots of quadratic equation X2 – kX + 27 = 0 is 3, then find the value of ‘k’
विकल्प
10
12
– 12
16
उत्तर
12
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If one of the roots of quadratic equation x2 + kx + 54 = 0 is – 6, then complete the following activity to find the value of ‘k’.
Activity: One of the roots of the quadratic equation x2 + kx + 54 = 0 is – 6.
Therefore let’s take x = ______
(– 6)2 + k(– 6) + 54 = 0
(______) – 6k + 54 = 0
– 6k + ______ = 0
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Determine whether (x – 3) is a factor of polynomial x3 – 19x + 30.
Let P(x) = x3 – 19x + 30
By remainder theorem, `square` will be a factor of P(x), if P(3) = 0
Now, P(3) = `square` – 19 `square` + 30
= `square – square` + 30
= `square – square`
= 0
∵ P(3) = 0
Hence, `square` is a factor of polynomial x3 – 19x + 30.
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One of the roots of equation x2 + 5x + a = 0 is – 3. To find the value of a, fill in the boxes.
Since, `square` is a root of equation x2 + 5x + a = 0
∴ Put x = `square` in the equation
⇒ `square^2 + 5 xx square + a` = 0
⇒ `square + square + a` = 0
⇒ `square + a` = 0
⇒ a = `square`
Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.
