Question

12. If the product of the zeros of the quadratic polynomial x - 4x + k is 3
then write the value of k.
13 IFC​

Answer 1

Answer:

k = 3/4

Step-by-step explanation:

P = c/a where polynomial is in form of ax^2 + bx + c

hence we put values and equate c term to product by the formula

X^2-Sx+P = p(x)

Answer 2

$\large{\underline{\bf{\pink{Answer:-}}}}$

✰ k = 3

$\large{\underline{\bf{\blue{Explanation:-}}}}$

✰ αβ = c/a

product of zeroes = constant term/coefficient of x².

$\large{\underline{\bf{\green{Given:-}}}}$

✰ p(x) = x² - 4x + k

✰ product of zeroes = 3

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the value of k.

$\huge{\underline{\bf{\red{Solution:-}}}}$

➜⠀⠀⠀⠀a = 1

➜⠀⠀⠀⠀ b = -4

➜⠀⠀⠀⠀c = k

$\bf:\implies\:\alpha\beta=\frac{c}{a}$

➜⠀⠀⠀⠀αβ = 3

➩⠀⠀⠀⠀⠀3 = k/1

➩⠀⠀⠀⠀⠀k = 3

varification:-

➩⠀⠀⠀⠀⠀x² - 4x + k

➩⠀⠀⠀⠀⠀x² - 4x + 3

➩⠀⠀⠀⠀⠀x² - x - 3x + 3

➩⠀⠀⠀⠀⠀x( x - 1) -3 (x - 1)

➩⠀⠀⠀⠀⠀(x -1)(x -3)

➩⠀⠀⠀⠀⠀x = 1 or x = 3

Let α = 1 and β = 3

α + β = 4

αβ = 3

Hence varified.

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