Practise questions · Salam Academy

SA-9709-P1-QD-0172 marksL1 FoundationCalculatorNature of roots

For the equation

2x^2-3x+5=0

, find the value of the discriminant and state the number of real roots.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0012 marksL1 FoundationCalculatorNature of roots

Find the discriminant of

3x^2-2x+5

and hence state the number of real roots of

3x^2-2x+5=0

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0022 marksL1 FoundationCalculatorUnknown constants

x^2+4x+k=0

has equal roots. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-G012 marksL1 FoundationCalculatorNature of roots

Find the discriminant of

x^2-6x+9

, and state how many real roots

x^2-6x+9=0

has.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-Q011 markL1 FoundationCalculatorNature of roots

The discriminant of

ax^2+bx+c

is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-Q021 markL1 FoundationCalculatorNature of roots

The curve

y=ax^2+bx+c

touches the

x

-axis without crossing it. Then

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-Q051 markL1 FoundationCalculatorNature of roots

A quadratic equation has discriminant

0

. How many real roots does it have?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0163 marksL2 StandardCalculatorNature of roots

Find the set of values of

k

for which

x^2+kx+9=0

has two distinct real roots. Give your answer in the form

k<a

or

k>b

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0032 marksL2 StandardCalculatorUnknown constants

Find the values of

k

for which

2x^2+kx+8=0

has equal roots.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0043 marksL2 StandardCalculatorUnknown constants

x^2-6x+k=0

has no real roots. The set of possible values of

k

is

k>a

. Find

a

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0053 marksL2 StandardCalculatorUnknown constants

kx^2+4x+1=0

, where

k\ne0

, has two distinct real roots. The set of possible values of

k

is

k<a

,

k\ne0

. Find

a

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0113 marksL2 StandardCalculatorAlways positive

2x^2-8x+k>0

for all real

x

. The set of possible values of

k

is

k>a

. Find

a

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0184 marksL3 ExamCalculatorNature of roots

The line

y=2x+k

is a tangent to the curve

y=x^2-4x+7

. Find the value of

k

and the

x

-coordinate of the point where the line touches the curve.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0253 marksL3 ExamCalculatorNature of roots

The equation

kx^2+6x+k=0

has a repeated root, where

k

is a positive constant. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0063 marksL3 ExamCalculatorUnknown constants

Find the values of

k

for which

x^2+(k+2)x+4=0

has a repeated root.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0074 marksL3 ExamCalculatorUnknown constants

Find the set of values of

k

for which

x^2+kx+k+3=0

has real roots. Give your answer as

k\le a

or

k\ge b

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0082 marksL3 ExamCalculatorAlways positive

For

x^2+2kx+k^2+1=0

, find the discriminant in its simplest form, and hence explain why the equation has no real roots for any value of

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0093 marksL3 ExamCalculatorUnknown constants

The line

y=2x+c

is a tangent to the curve

y=x^2+4

. Find

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0104 marksL3 ExamCalculatorUnknown constants

The line

y=mx-1

does not meet the curve

y=x^2+3

. The set of possible values of

m

is

a<m<b

. Find

a

and

b

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD3-0123 marksL3 ExamCalculatorUnknown constants

(k-1)x^2+2kx+(k+2)=0

has a repeated root. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

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