Educational

Find the Value of p for Which the Quadratic Equation Has Equal Roots and Also Find the Roots Question: \( (p+1)x^2 – 6(p+1)x + 3(p+9) = 0,\; p \ne -1 \) Find the value of \(p\) for which the equation has equal roots. Also, find the roots. Solution For equal roots, the discriminant must be […]

If 1 is a Root of 3x² + ax − 2 = 0 and a(x² + 6x) − b = 0 Has Equal Roots, Find b Question: If \(1\) is a root of the quadratic equation \(3x^2+ax-2=0\) and the quadratic equation \(a(x^2+6x)-b=0\) has equal roots, find the value of \(b\). Solution Since \(1\) is a

If 2 is a Root of 3x² + px − 8 = 0 and 4x² − 2px + k = 0 Has Equal Roots, Find k Question: If \(2\) is a root of the quadratic equation \(3x^2+px-8=0\) and the quadratic equation \(4x^2-2px+k=0\) has equal roots, find the value of \(k\). Solution Since \(2\) is a

If −5 is a Root of 2x² + px − 15 = 0 and p(x² + x) + k = 0 Has Equal Roots, Find k Question: If \( -5 \) is a root of the quadratic equation \( 2x^2+px-15=0 \) and the quadratic equation \( p(x^2+x)+k=0 \) has equal roots, find the value of

Find the Values of p for Which the Quadratic Equation Has Equal Roots. Also, Find These Roots. Question: \( (2p+1)x^2-(7p+2)x+(7p-3)=0 \) Find the values of \(p\) for which the equation has equal roots. Also, find these roots. Solution For equal roots, the discriminant must be zero. \( D=b^2-4ac=0 \) Here, \( a=2p+1,\quad b=-(7p+2),\quad c=7p-3 \)

Write All the Values of k for Which x² + kx + 16 = 0 Has Equal Roots. Find the Roots of the Equation So Obtained. Question: \( x^2 + kx + 16 = 0 \) Write all the values of \(k\) for which the equation has equal roots. Find the roots of the equation

Find the Value of k for Which the Quadratic Equation Has Equal Roots and Also Find the Roots Question: \( (3k+1)x^2 + 2(k+1)x + 1 = 0 \) Find the value of \(k\) for which the equation has equal roots. Also, find the roots. Solution For equal roots, the discriminant must be zero. \( D=b^2-4ac=0

Find the Least Positive Value of k for Which the Equation x² + kx + 4 = 0 Has Equal Roots Question: \( x^2 + kx + 4 = 0 \) Find the least positive value of \(k\) for which the equation has equal roots. Solution For equal roots, the discriminant must be zero. \(

For What Value of k is the Given Quadratic Equation a Perfect Square? Question: \( (4-k)x^2+(2k+4)x+(8k+1)=0 \) Find the value of \(k\) for which the quadratic equation is a perfect square. Solution A quadratic expression is a perfect square when its discriminant is zero. \( D=b^2-4ac=0 \) Here, \( a=4-k,\quad b=2k+4,\quad c=8k+1 \) Substituting in

Find the Values of k for Which the Given Quadratic Equation Has Real and Distinct Roots Question: \( kx^2 + 6x + 1 = 0 \) Find the values of \(k\) for which the above quadratic equation has real and distinct roots. Solution For real and distinct roots, the discriminant must be positive. \( D