If one zero of the polynomial x² - 12x + (3k-1) is five times the other then the value of k is : *
Answers
Let one zero of polynomial is t.
Then other zero will be 5t
The sum of two zeros of a polynomial = -b/a = 5/3
⇒t +5t=5/3
⇒6t=5/3
⇒t=5/18
⇒t=5/18 (1)
The multiplication of zeros = c/a = (2k+1)/3
5t×t=(2k+1)/3
5(5/18)^2 = (2k+1)/3
125/324=(2k+1)/3
125=108(2k+1)
125=216k +108
216k=17
k=17/216
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SOLUTION
GIVEN
One zero of the polynomial x² - 12x + (3k-1) is five times the other
TO DETERMINE
The value of k
EVALUATION
Here the given Quadratic polynomial is
x² - 12x + (3k-1)
Comparing with the general quadratic polynomial ax² + bx + c we get a = 1 , b = - 12 , c = 3k - 1
Now it is given that one zero of the polynomial is five times the other
Let the zeroes are α and 5α
Sum of the zeroes = - b/a
⇒ α + 5α = 12/1
⇒ 6α = 12
⇒ α = 2
So the zeroes are 2 and 10
Now
Product of the zeroes = c/a
⇒ 2 × 10 = 3k - 1
⇒ 3k - 1 = 20
⇒ 3k = 21
⇒ k = 7
FINAL ANSWER
Hence the required value of k = 7
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