Question

6x2 (15x2 + x - 6) ÷ 3x(3x + 2)​

Answer 1

Answer :

10x² - 6x

Step-by-step explanation :

          $=\frac{6x^{2} (15x^{2} +x-6)}{3x(3x+2)} \\\\\\ =\frac{6x^2(15x^2+10x-9x-6)}{3x(3x+2)} \\\\\\ =\frac{6x^2[5x(3x+2)-3(3x+2)]}{3x(3x+2)} \\\\\\ =\frac{6x^2[(3x+2)(5x-3)]}{3x(3x+2)} \\\\\\ =\frac{6x^2}{3x} \times\frac{(3x+2)(5x-3)}{3x+2} \\\\\\ =2x \times (5x-3) \\\\\\ =10x^2-6x$

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     Quadratic Polynomials :

         ✯ It is a polynomial of degree 2

         ✯ General form :

                   ax² + bx + c  = 0

                    $\boxed{\bf x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }$

         ✯ Determinant, D = b² - 4ac

         ✯ Based on the value of Determinant, we can define the nature of roots.

                 D > 0 ; real and unequal roots

                 D = 0 ; real and equal roots

                 D < 0 ; no real roots i.e., imaginary

         ✯ Relationship between zeroes and coefficients :

                   ✩ Sum of zeroes = -b/a

                   ✩ Product of zeroes = c/a

Answer 2

Given

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$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{6x^2(15x^2 + x - 6)}{3x(3x + 2)}}$

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Solution

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$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{6x^2(15x^2 + x - 6)}{3x(3x + 2)}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{6x^2(15x^2 +10x - 9x - 6)}{3x(3x + 2)}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{6x^2[5x(3x + 2) -3(3x + 2)]}{3x(3x + 2)}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{6x^2[(5x - 3)(3x + 2)]}{3x(3x + 2)}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{6x^2}{3x} × \dfrac{(5x - 3)\not{(3x + 2)}}{\not{(3x + 2)}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {2x × (5x - 3)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {10x^2 - 6x}$

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