Ravi Kant Kumar

Determine the Nature of Roots of 2x² − 6x + 3 = 0 Determine the Nature of Roots of the Quadratic Equation 2x² − 6x + 3 = 0 Solution Given: $$2x^2-6x+3=0$$ Here, $$a=2,\quad b=-6,\quad c=3$$ Using the discriminant, $$D=b^2-4ac$$ $$D=(-6)^2-4(2)(3)$$ $$D=36-24=12$$ Since $$D>0,$$ the roots are real and distinct. Answer The equation 2x² − […]

Determine the Nature of Roots of 2x² − 3x + 5 = 0 Determine the Nature of Roots of the Quadratic Equation 2x² − 3x + 5 = 0 Solution Given: $$2x^2-3x+5=0$$ Here, $$a=2,\quad b=-3,\quad c=5$$ Using the discriminant, $$D=b^2-4ac$$ $$D=(-3)^2-4(2)(5)$$ $$D=9-40=-31$$ Since $$D

RD Sharma Chapter 4 : Quadratic Equation – Exercise 4.6 Solutions (Step-by-Step Guide) Determine the nature of the roots of the following quadratic equations:   (i) 2x² − 3x + 5 = 0 Watch Solution   (ii) 2x² − 6x + 3 = 0 Watch Solution   (iii) (3/5)x² − (2/3)x + 1 = 0 Watch

Solve for x : 1/(x − 3) − 1/(x + 5) = 1/6 Solve for x : 1/(x − 3) − 1/(x + 5) = 1/6 Question Solve for x: \[ \frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}, \qquad x\ne3,-5 \] Solution Taking LCM on the left side, \[ \frac{(x+5)-(x-3)}{(x-3)(x+5)} = \frac{1}{6} \] \[ \frac{8}{(x-3)(x+5)} = \frac{1}{6} \] Cross multiplying, \[

Solve for x : 16/x − 1 = 15/(x + 1) Solve for x : 16/x − 1 = 15/(x + 1) Question Solve for x: \[ \frac{16}{x}-1=\frac{15}{x+1}, \qquad x\ne0,-1 \] Solution Multiplying both sides by \(x(x+1)\), \[ 16(x+1)-x(x+1)=15x \] \[ 16x+16-x^2-x=15x \] \[ -x^2+16=0 \] \[ x^2-16=0 \] \[ (x-4)(x+4)=0 \] \[ x=4 \]

Solve for x : x + 1/x = 3 Solve for x : x + 1/x = 3 Question Solve for x: \[ x+\frac{1}{x}=3, \qquad x\ne0 \] Solution Multiplying both sides by \(x\), \[ x^2+1=3x \] \[ x^2-3x+1=0 \] Using the quadratic formula, \[ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \] \[ x=\frac{3\pm\sqrt{9-4}}{2} \] \[ x=\frac{3\pm\sqrt5}{2} \] Answer \[ \boxed{x=\frac{3+\sqrt5}{2}\quad

Solve for x : 1/x + 2/(2x − 3) = 1/(x − 2) Solve for x : 1/x + 2/(2x − 3) = 1/(x − 2) Question Solve for x: \[ \frac{1}{x}+\frac{2}{2x-3}=\frac{1}{x-2}, \qquad x\ne0,\frac{3}{2},2 \] Solution Multiplying both sides by \(x(2x-3)(x-2)\), \[ (2x-3)(x-2)+2x(x-2)=x(2x-3) \] \[ 2x^2-7x+6+2x^2-4x=2x^2-3x \] \[ 2x^2-8x+6=0 \] \[ x^2-4x+3=0 \] \[ (x-1)(x-3)=0

Solve (x-1)/(x-2) + (x-3)/(x-4) = 3⅓ for x Solve \((x-1)/(x-2) + (x-3)/(x-4) = 3\frac{1}{3}\) for x Question Solve for x: \[ \frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3}, \qquad x\ne2,4 \] Solution \[ \frac{x-1}{x-2}+\frac{x-3}{x-4}=\frac{10}{3} \] Multiplying both sides by \(3(x-2)(x-4)\), \[ 3(x-1)(x-4)+3(x-3)(x-2) = 10(x-2)(x-4) \] \[ 3(x^2-5x+4)+3(x^2-5x+6) = 10(x^2-6x+8) \] \[ 6x^2-30x+30 = 10x^2-60x+80 \] \[ 4x^2-30x+50=0 \] \[ 2x^2-15x+25=0 \]

Determine Whether 2x² − 2√2x + 1 = 0 Has Real Roots and Find the Roots Determine Whether 2x² − 2√2x + 1 = 0 Has Real Roots and Find the Roots Question Determine whether the given quadratic equation has real roots and if so, find the roots: \[ 2x^2-2\sqrt2x+1=0 \] Solution \[ a=2,\quad b=-2\sqrt2,\quad

Determine Whether 3x² − 5x + 2 = 0 Has Real Roots and Find the Roots Determine Whether 3x² − 5x + 2 = 0 Has Real Roots and Find the Roots Question Determine whether the given quadratic equation has real roots and if so, find the roots: \[ 3x^2-5x+2=0 \] Solution \[ a=3,\quad b=-5,\quad