Question

Find the value of x:
21x^2 - 83x + 34 = 0
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Please solve this problem frnds and show the steps along with your answer.....Otherwise, don't give the answer.

Answer 1

21x²-83x+34=0
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Multiply first and last term i.e.,21×34=>714
Now factorise 714=>2,3,7,14
Adding (2×3×7+14)=>(42+14)=>83(Middle term)
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So,
→21x²-42x-17x+34=0
→21x(x-2)-17(x-2)=0
→(21x-17)(x-2)=0
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21x-17=0
21x=17
x=17/21

x-2=0
x=2
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Hence two value of x is 17/21 and 2

Answer 2

Answer: In the quadratic equation $21x^{2} -83x+34 = 0$ value of x is 2 and $\frac{17}{21}$.

Step-by-step explanation:

Given:The given quadratic equation is $21x^{2} -83x+34 = 0$.

To find:We have to find the value of x.

Step 1:As we have given$21x^{2} -83x+34 = 0$.To find the factor given expression we have to write middle term$-83x$ into two terms such that the multiplication of two terms should be equal to product of first term and and third term and their addition or subtraction should be the middle term.

Step 2:So the multiplication of two term should be 714 and their addition or subtraction should be .

Step 3:So we have,

⇒                $21x^{2} -83x+34 = 0$

⇒      $21x^{2} -42x-17x+34 = 0$

⇒      $21x(x-2)-17(x-2) = 0$

⇒              $(x-2)(21x-17) = 0$

Step 4:Now to find the value of x we have,

⇒             $x-2 = 0$

⇒                   $x = 2$

and

⇒       $21x-17 = 0$  

⇒               $21x = 17$    

⇒                  $x = \frac{17}{21}$  

∴ In the quadratic equation $21x^{2} -83x+34 = 0$ value of x is 2 and $\frac{17}{21}$.

Splitting the Middle Term for Factoring Quadratics:

The sum of the roots of the equation  can be given by,

α+β = -b/a

The product of the roots in the equation   can be given by,

α.β = c/a

We split the middle term b of the quadratic equation such that when we try to factorize quadratic equations. We determine the factor pairs of the product of a and c such that their sum is equal to b.