A quadratic is ax2+bx+c=0 β the highest power is 2, so it has up to two roots. SSC rarely asks you to fully solve one; instead it tests two quick ideas: when the roots are equal, and how the roots relate to b and c.
The two ideas that score the marks
β’ Discriminant for equal roots: the roots are equal exactly when D=b2β4ac=0. Read off a,b,c (keep the signs), set b2=4ac, and solve.
β’ Sum & product of roots: for x2+bx+c=0, the roots add to βb and multiply to c. If the roots are in ratio m:n, call them mΞ± and nΞ±, use the sum to find Ξ±, then the product.
β’ Factor theorem: if (xβr) is a factor, then putting x=r makes the polynomial zero β substitute and solve for the unknown.
Shortcut for equal roots: with leading coefficient 1, the constant must equal (2bβ)2; if a=c, equal roots mean b=Β±2a.
For equal roots of x2β4x+a=0: 16β4a=0, so a= .
πPractice Questions
Q1For equal roots of xΒ² β 6x + k = 0, find k.
Q2If (x β 1) is a factor of xΒ² + ax β 3, find a.
Q3The roots of xΒ² + 7x + 12 = 0 are:
π
Real exam questions β Quadratic Equations
2 question types Β· 7 solved examples from real SSC papers
Most quadratic PYQs test one of two ideas: the discriminant for equal roots, and sum/product of roots (with the factor theorem). Both are plug-and-go.
How to solve this type
Equal roots happen exactly when the discriminant D=b2β4ac=0. Read off a, b, c (keep signs), set b2=4ac, and solve. A handy shortcut: if a=1, equal roots mean the constant is (2bβ)2; if a=c, equal roots mean b=Β±2a.
If the roots of x2β4x+a=0 are equal, find a.
Aβ8B8Cβ4D4
For equal roots of 2x2β8x+k=0, find k.
A2B4C8D16
For what positive k does 3x2+2kx+3=0 have real, equal roots?
