1. Check whether the following are quadratic equations
((x+1)=2(x-3)
Answers
Answer:
X+1=2x -6
6-1 =2x -1x
5= X
no it's a linear equations
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Answer:
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Step-by-step explanation:
(i) (x + 2)2 2(x - 3) → x2 + 2x + 1 = 2x - 6 X2 + 7 = 0
It is of the form ax2 + bx + c = 0. Hence, the given equation is quadratic
equation.
(ii) x2 - 2x = (-2)(3 :
→ x2 - 2x = -6 + 2x
» x2 - 4x + 6 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is quadratic equation.
(iii) (x - 2)(x + 1) = (x - 1)(x + 3) X2 - x - 2 = x2 + 2x - 3
→ 3x - 1 =0
It is not of the form ax2 + bx + c = 0. Hence, the given equation is not a quadratic equation.
(iv) (x - 3)(2x + 1) = x(x + 5)
- 2x2 5x - 3 = x2 + 5x It is of the form ax2 + bx + c = 0. Hence, the given equation is quadratic
equation.
(V) (2x - 1)(x - 3) = (x + 5)(x - 1)
- 2x2 - 7x + 3 = x2 + 4x - 5 → x2 - 11x + 8 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is quadratic
equation.
(vi) x2 + 3x 1= (x - 2)2 → x2 + 3x + 1 = x2 + 4 - 4x
+
- 7x - 3 = O It is not of the form ax2 + bx + c = 0.
Hence, the given equation is not a quadratic equation.
(vii) (x + 2)3 = 2x(x2 - 1) x3 + 8x2 + 12x = 2x3 - 2x
→ x3 + 14x - 6x2 - 8 = O It is not of the form ax2 + bx + c = 0.
Hence, the given equation is not a quadratic equation.
(viii) 3 - 4x2 - x + 1 = (x - 2)3
→ x3 - 4x2 - x +1= x3 - 8 - 6x2 + 12x
2x2 13x + 9 = 0 It is of the form ax2 + bx + c = 0.
Hence, the given equation is quadratic equation.