Find the zeros of the following quadratic equations and verify relationship between the zeroes and coefficients.
3√3x²-19x+10√3
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Find the zeros of the following quadratic equations and verify relationship between the zeroes and coefficients.
3√3x²-19x+10√3
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Given quadratic equations is 3√3x² - 19x + 10√3
Now, solve it by splitting the middle term
We have to find zeros. So,
⇒ 3√3x² - 19x + 10√3 = 0
⇒ 3√3x² - 9x - 10x + 10√3 = 0
⇒ 3√3x(x - √3) - 10(x - √3) = 0
⇒ (3√3x - 10)(x - √3) = 0
On comparing we get,
⇒ x = 10/3√3, √3
Therefore, zeros are 10/3√3 and √3
Verification
In quadratic polynomial 3√3x² - 19x + 10√3
a = 3√3, b = -19 and c = 10√3
Sum of zeros = -b/a
10/3√3 + √3 = -(-19)/3√3
(10 + 9)/3√3 = 19/3√3
19/3√3 = 19/3√3
Product of zeros = c/a
(10/3√3)(√3) = 10√3/3√3
10/3 = 10/3