🌾 Agricultural Engineer Career in India Agriculture + Engineering = A Future-Ready Career क्या आपको Science, Technology, Machines और Farming में interest है? तो Agricultural Engineering आपके लिए एक interesting career option हो सकता है। Agricultural Engineers engineering principles और modern technology का use करके agriculture sector की problems का practical solution […]

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