Question

find the zeros of xaquare-5x + 6 the relationships between zeros and its coeffetients​

Answer 1

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alishaagra99

alishaagra99

30.05.2017

Math

Secondary School

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find the zeros of the quadratic polynomial(x2 5x 6) and verify the relation between the zeroes and the coefficients

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book2 avatar

the question is not clear

book2 avatar

is it x^2+5x+6

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fadiguddi

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it is sufficient for your question

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mysticd

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Explanation:

We have the quadratic polynomial x²+5x+6

splitting the middle term, we get

= x²+2x+3x+6

= x(x+2)+3(x+2)

= (x+2)(x+3)

So, the values of x²+5x+6 is zero when x+2=0 Or x+3=0

i.e ., when x = -2 Or x = -3

Therefore, the zeroes of x²+5x+6 are -2 and -3

Now ,

Verification:

i)the sum of the Zeroes = -2+(-3)

= -5

= (-5)/1

=

ii) Product of the zeroes

= (-2)(-3)

= 6

= 6/1

=

Step-by-step explanation:

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Answer 2

Solution :

We have quadratic polynomial p(x) = x² - 5x + 6 & zero of the polynomial p(x) = 0;

$\underline{\underline{\tt{Using\:\:by\:\:factorization\:\:method\::}}}$

$\longrightarrow\sf{x^{2} -5x + 6=0}$

$\longrightarrow\sf{x^{2} -2x -3x + 6=0}$

$\longrightarrow\sf{x(x-2) -3(x-2) = 0}$

$\longrightarrow\sf{(x-2)(x-3)=0}$

$\longrightarrow\sf{x-2=0\:\:\:Or\:\:\:x-3=0}$

$\longrightarrow\bf{x=2\:\:\:Or\:\:\:x=3}$

∴ α = 2 & β = 3 are the zeroes of the given polynomials .

As we know that given quadratic polynomial compared with ax² + bx + c, where as;

• a = 1
• b = -5
• c = 6

Now;

$\underline{\mathcal{SUM\:OF\:THE\:ZEROES\::}}$

$\mapsto\tt{\alpha + \beta =\dfrac{-b}{a} =\bigg\lgroup \dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2}}\bigg\rgroup }\\\\\\\mapsto\tt{2 + 3 = \dfrac{-(-5)}{1} }\\\\\\\mapsto\bf{5=5}$

$\underline{\mathcal{PRODUCT\:OF\:THE\:ZEROES\::}}$

$\mapsto\tt{\alpha \times \beta =\dfrac{c}{a} =\bigg\lgroup \dfrac{Constant\:term}{Coefficient\:of\:x^{2}}\bigg\rgroup }\\\\\\\mapsto\tt{2 \times 3 = \dfrac{6}{1} }\\\\\\\mapsto\bf{6=6}$

Thus;

The relationship between zeroes & coefficient are verified .