If one of the zeros of the quadratic polynomial f(x)=14x²-42k²x-9 is negative find the value of k
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f (x) = 14 x² - 42 k² x - 9
root = [ 42 k² + - √ (42² k⁴ + 504) ] / 28
= 3 * [ 7 k² + - √(7² k⁴ + 14) ] / 14
since k² is non negative,
7 k² < √ (7 k⁴ + 14)
so we will have one root negative and one root positive.
This is true for any real value of k.
root = [ 42 k² + - √ (42² k⁴ + 504) ] / 28
= 3 * [ 7 k² + - √(7² k⁴ + 14) ] / 14
since k² is non negative,
7 k² < √ (7 k⁴ + 14)
so we will have one root negative and one root positive.
This is true for any real value of k.
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Answered by
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Answer:HEY MATE
Step-by-step explanation:
Comparing f(x) = 4x2 - 8kx - 9 with ax2+bx+c we get
a=4; b=-8k and c=-9.
Since one root is the negative of the other, let us assume that the roots are p an -p.
Sum of the roots, a+(-a)=-b/a= - (-8k) / 4
0=2k
k=0
HOPE THIS HELPED YOU........
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