Find the zeros of the polynomialx^2+1/6x-2 …
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Find the zeros of the polynomialx^2+1/6x-2 and verify the relationship between the efficient and the zeros of the polynomial.
Posted by Lava Partap 8 years, 4 months ago
- 2 answers
Payal Singh 8 years, 4 months ago
Polynomial : {tex}x^2+{1\over 6}x-2{/tex}
Comparing with standard equation, we get
a = 1, b = {tex}{1\over 6}{/tex} , c = -2
To find zero, equate it with 0
{tex}=> x^2+{1\over 6}x-2 = 0{/tex}
Multiply by 6
{tex}=> 6x^2+x-12 = 0{/tex}
{tex}=> 6x^2+9x-8x-12 = 0{/tex}
=> 3x(2x+3) - 4(2x+3) = 0
=> (2x+3)(3x-4) = 0
2x+3 = 0 Or 3x-4 = 0
=> x = {tex}-{3\over2} \ or \ {4\over 3}{/tex}
We know
Sum of zeroes = {tex}{-b\over a}{/tex}
=> {tex}-{3\over 2} + {4\over 3} = -{1\over 6}{/tex}
=> {tex}{-9+8\over 6} = -{1\over 6}{/tex}
=> {tex}-{1\over 6} = -{1\over 6} {/tex}
Also
Product of zeroes = {tex}c\over a{/tex}
=> {tex}-{3\over 2}\times {4\over 3}={-2\over 1}{/tex}
=> -2 = -2
Hence verified
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Jyoti Kashyap 4 years, 8 months ago
0Thank You