Question

Solve x2-7x+5=0 by factorization method

Answer 1

Answer:

Step-by-step explanation:

X^2-7x+5

X^2-5x-2x+5

X(2x-5) -1(2x-5)

(2x-5) ( x-1)

Answer 2

$\huge\underline\mathfrak\red{Question :}$

Solve

${x}^{2} - 7x + 5 = 0$

by using factorization method

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$\huge\underline\mathfrak\blue{Answer :}$

$\underline\mathfrak\pink{solution \ of \ this \ problem \ using }$

$\underline\mathfrak\pink{quadratic \ formula }$

$\underline\mathfrak\orange{Solution 1 : }$

$\frac{7 + \sqrt{29} }{2} = 6.193$

$\underline\mathfrak\orange{Solution 2 : }$

$\frac{7 - \sqrt{29} }{2} = 0.805$

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$\huge\underline\mathfrak\green{Solution :}$

$\sf\large\underline\pink{Given:}$

We're given the quadratic equation

${x}^{2} - 7x + 5 = 0$

$\sf\large\underline\pink{Note:}$

$\underline\mathfrak\green{Let's \ try \ to \ solve \ this \ problem }$

[/tex]

$\underline\mathfrak\green{ by \ using \ factorization \ method}$

⇒The first term is, ${x}^{2}$, it's coefficient is 1.

⇒Middle term is, $- 7x$ ,it's coefficient is –7.

⇒The last term ,"The Constant" , is –5.

➨$\sf\large\underline{Step 1 :}$Multiply the coefficient of the first term by the constant 1 • 5 = 5

➨$\sf\large\underline{Step 2 :}$ Find two factors of 5 whose sum equals the coefficient of the middle term, which is -7

-5 + -1 = -6

-1 + -5 = -6

1 + 5 = 6

5 + 1 = 6

$\underline\mathfrak\green{No \ two \ such \ factors \ can \ be \ found !!}$

$\underline\mathfrak\pink{This \ equation \ can't \ be \ factorised }$

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$\underline\mathfrak\green{Let's \ solve \ this \ problem \ using \ quadratic \ formula }$

Given, Quadratic equation is ${x}^{2} - 7x + 5$

Compare this equation with $A{x}^{2} + Bx + C = 0$

⇒where A, B and C are numbers, often called coefficients, is given by

$x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a}$

In our case, A = 1

B = -7

C = 5

➨Accordingly,

⇒${B}^{2} - 4AC=$

⇒$49 - 20 =$

⇒$29$

➨Applying the quadratic formula :

$x = \frac{7± \sqrt{29} }{2}$

√ 29 , rounded to 4 decimal digits, is 5.3852

⇒So now we are looking at:

$x = \frac{7± 5.385}{2}$

⇒Two real solutions:

$x = \frac{7 + \sqrt{29} }{2} = 6.193$

or

$x = \frac{7 - \sqrt{29} }{2} = 0.807$

$\underline\mathfrak\green{Two \ solutions \ of \ the \ equations \ are :}$

⟾$\underline\mathfrak\orange{Solution 1 : }$

⬤$\frac{7 + \sqrt{29} }{2} = 6.193$

⟾$\underline\mathfrak\orange{Solution 2 : }$

⬤$\frac{7 - \sqrt{29} }{2} = 0.805$

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hope it helps :))