Ravi Kant Kumar

Find the Value of k for Which the Roots Are Real and Equal in 2kx² − 40x + 25 = 0 Find the Value of k for Which the Roots Are Real and Equal Solution Given: $$2kx^2-40x+25=0$$ Here, $$a=2k,\quad b=-40,\quad c=25$$ For real and equal roots, $$D=b^2-4ac=0$$ $$(-40)^2-4(2k)(25)=0$$ $$1600-200k=0$$ $$200k=1600$$ $$k=8$$ Answer The value of […]

Find the Value of k for Which the Roots Are Real and Equal in 4x² + kx + 9 = 0 Find the Value of k for Which the Roots Are Real and Equal Solution Given: $$4x^2+kx+9=0$$ Here, $$a=4,\quad b=k,\quad c=9$$ For real and equal roots, $$D=b^2-4ac=0$$ $$k^2-4(4)(9)=0$$ $$k^2-144=0$$ $$k^2=144$$ $$k=\pm12$$ Answer The value(s) of

Find the Value of k for Which the Roots Are Real and Equal in 3x² − 5x + 2k = 0 Find the Value of k for Which the Roots Are Real and Equal Solution Given: $$3x^2-5x+2k=0$$ Here, $$a=3,\quad b=-5,\quad c=2k$$ For real and equal roots, $$D=b^2-4ac=0$$ $$(-5)^2-4(3)(2k)=0$$ $$25-24k=0$$ $$k=\frac{25}{24}$$ Answer The value of k

Find the Value of k for Which the Roots Are Real and Equal in kx² − 2√5x + 4 = 0 Find the Value of k for Which the Roots Are Real and Equal Solution Given: $$kx^2-2\sqrt{5}x+4=0$$ Here, $$a=k,\quad b=-2\sqrt{5},\quad c=4$$ For real and equal roots, $$D=b^2-4ac=0$$ $$(-2\sqrt{5})^2-4(k)(4)=0$$ $$20-16k=0$$ $$k=\frac{20}{16}=\frac{5}{4}$$ Answer The value of k

Find the Value of k for Which the Roots Are Real and Equal in kx² + 4x + 1 = 0 Find the Value of k for Which the Roots Are Real and Equal Solution Given: $$kx^2+4x+1=0$$ Here, $$a=k,\quad b=4,\quad c=1$$ For real and equal roots, $$D=b^2-4ac=0$$ $$4^2-4(k)(1)=0$$ $$16-4k=0$$ $$k=4$$ Answer The value of k

Determine the Nature of Roots of 4x² + 4√3x + 3 = 0 Determine the Nature of Roots of the Quadratic Equation 4x² + 4√3x + 3 = 0 Solution Given: $$4x^2+4\sqrt{3}x+3=0$$ Here, $$a=4,\quad b=4\sqrt{3},\quad c=3$$ Using the discriminant, $$D=b^2-4ac$$ $$D=(4\sqrt{3})^2-4(4)(3)$$ $$D=48-48=0$$ Since $$D=0,$$ the roots are real and equal. Answer The equation 4x² +

Determine the Nature of Roots of 3x² − 2√6x + 2 = 0 Determine the Nature of Roots of the Quadratic Equation 3x² − 2√6x + 2 = 0 Solution Given: $$3x^2-2\sqrt{6}x+2=0$$ Here, $$a=3,\quad b=-2\sqrt{6},\quad c=2$$ Using the discriminant, $$D=b^2-4ac$$ $$D=(-2\sqrt{6})^2-4(3)(2)$$ $$D=24-24=0$$ Since $$D=0,$$ the roots are real and equal. Answer The equation 3x² −

Determine the Nature of Roots of 3x² − 4√3x + 4 = 0 Determine the Nature of Roots of the Quadratic Equation 3x² − 4√3x + 4 = 0 Solution Given: $$3x^2-4\sqrt{3}x+4=0$$ Here, $$a=3,\quad b=-4\sqrt{3},\quad c=4$$ Using the discriminant, $$D=b^2-4ac$$ $$D=(-4\sqrt{3})^2-4(3)(4)$$ $$D=48-48=0$$ Since $$D=0,$$ the roots are real and equal. Answer The equation 3x² −

Determine the Nature of Roots of (3/5)x² − (2/3)x + 1 = 0 Determine the Nature of Roots of the Quadratic Equation (3/5)x² − (2/3)x + 1 = 0 Solution Given: $$\frac{3}{5}x^2-\frac{2}{3}x+1=0$$ Here, $$a=\frac{3}{5},\quad b=-\frac{2}{3},\quad c=1$$ Using the discriminant, $$D=b^2-4ac$$ $$D=\left(-\frac{2}{3}\right)^2-4\left(\frac{3}{5}\right)(1)$$ $$D=\frac{4}{9}-\frac{12}{5}$$ $$D=\frac{20-108}{45}=-\frac{88}{45}$$ Since $$D

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 −