(1)-1 (1) Find the value of k for which x= 1 is a root of the equation xsquare+Kx+3=0, Also find the other root
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Required Answer :
- The value of k = - 4
- The other root of the equation = 3
Given :
- x = 1 is a root of the equation x² + kx + 3 = 0
To find :
- The value of k
- The value of the other root of the equation
Solution :
Finding the value of k :
⇒ x² + kx + 3 = 0
Substitute the value of x in the equation :
⇒ (1)² + k(1) + 3 = 0
⇒ 1 + k + 3 = 0
⇒ k + 4 = 0
⇒ k = - 4
The value of k = - 4
Finding the other root :
Substitute the value of k in the equation :
⇒ x² + kx + 3 = 0
⇒ x² + (-4)x + 3 = 0
⇒ x² - 4x + 3 = 0
⇒ Product of the quadratic equation = 3x²
⇒ x² - 3x - 1x + 3 = 0
⇒ x(x - 3) - 1(x - 3) = 0
⇒ (x - 1)(x - 3) = 0
⇒ (x - 1) = 0 or (x - 3) = 0
⇒ x - 1 = 0 or x - 3 = 0
⇒ x = 1 or x = 3
Therefore, the other root of the equation = 3
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